The U. S. Constitution’s Second Amendment gives citizens the right to bear arms. Newspaper columnist and humorist Bill Vaughan (1915-1977) was credited in 1966 with turning the words around:
 
“Bill Vaughan says everyone is talking about their right to bear arms. He thinks hunting would be more lively if there was a right to arm bears.”
 
“Support the Right to Arm Bears” was cited as a bumper sticker slogan in 1972. In March 1974, a newspaper column stated that the “Support the Right to Arm Bears” bumper stickers were produced by Friends of Animals (established in New York in 1957). Cleveland Amory, a popular author and TV Guide columnist, founded The Fund for Animals (established in New York in 1967), a group also known for its “Support the Right to Arm Bears” bumper stockers and pins. “Support Your Right to Arm Bears” is a chapter title in Amory’s book, Man Kind?: Our Incredible War on Wildlife (1974). The animal-rights slogan attempts to stop the killing of bears and other animals.
     
 
Wikipedia: Cleveland Amory
Cleveland Amory (September 2, 1917 – October 14, 1998) was an American author who devoted his life to promoting animal rights. He was perhaps best known for his books about his cat, named Polar Bear, whom he saved from the Manhattan streets on Christmas Eve 1977. The executive director of the Humane Society of the United States described Amory as “the founding father of the modern animal protection movement.”
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While he spent considerable time as an outspoken reporter and advocate, he still remained committed to his organization Fund for Animals. The Fund struggled during the first decade or so of its existence, but by the time Amory died in 1998, it had a “$2 million budget, more than 200,000 members, and three animal sanctuaries, and had initiated several highprofile animal rescues, including the organic “painting” of baby harp seals off the Magdelene Islands in Canada to ensure that their fur was worthless to hunters.”
   
13 August 1966, The Gazette (Emporia, KS), “Smiles,” pg. 4, cols. 1-2:
Bill Vaughan says everyone is talking about their right to bear arms. He thinks hunting would be more lively if there was a right to arm bears.
 
4 December 1972,  Omaha (NE) World-Herald, “A Smile or Two,” pg. 18, col. 2:
Antihunter’s bumper sticker: “Support the Right to Arm Bears.”—Monroe County (Wis.) Democrat.
     
15 March 1974, The Evening Times (Trenton, NJ), “ActionLine,” pg. 17, col. 1:
Yes, we got our sticker (“I Brake For Animals—ed.) and you’ll be getting yours. Alice Herrington, president of Friends of Animals Inc., at 11 West 60th Street, New York, N. Y., 10023, says two sets apparently have been mailed and apparently lost. She personally mailed a third set after we signaled her.
 
By the way, group has another catchy sticker out aimed at hunters. It’s a red, white and blue circle proclaiming, “Support The Right To Arm Bears.” Friends of Animals believes that hunting and trapping animals is similar to murder and should be abolished. “Whatever the argument about the right to bear arms, one thing is certain: there is nothing in the Constitution which gives any person the right to murder animals,” group says.
 
Google Books
Man Kind?:
Our Incredible War on Wildlife
By Cleveland Amory
New York, NY: Harper & Row
1974
Pg. 7:
Support Your Right to Arm Bears.
 
Google News Archive
16 November 1974, Pittsburgh (PA) Press, “For Children’s Hospital benefit: 5 Authors Spell Good Time At Book Dinner” by Sylvia Sachs, Living, pg. 18, col. 3:
They pinned on the “Support Your Right to Arm Bears” buttons of Cleveland Amory.
 
Google News Archive
6 December 1974, Miami (FL) News, “Hunters are called ‘a bunch of creeps’ by Terry Johnson King, pg. 1B, col. 1:
As to the National Rifle Association’s insistence on the right to bear arms against animals, he (Cleveland Amory—ed.) simply turns loose his wit.
 
“Support Your Right to Arm Bears” is his slogan, and wherever he goes he wears a large pin bearing the phrase.
 
14 May 1980, Boston (MA) Globe, “Wearing your heart on your bumper” by Margo Miller, Living, pg. 1:
Battles are fought with bumper stickers: The National Rifle Assn. proclaims the “Right to Bear Arms” and the Fund for Animals demands the “Right To Arm Bears.”
 
OCLC WorldCat record
The right to bear arms : the right to arm bears = Het recht ons te bewapenen : wapen ons tegen het recht
Author: URSAAF (Amsterdam)
Publisher: Amsterdam : URSAAF-collectief, 1989.
Series: Bear necessities of life? = Eerste levensbehoeften?, vol. 12, no. 7. 
Edition/Format: Book : English
 
OCLC WorldCat record
“Support Your Right to Arm Bears (and Peccadillos)”: The Higher Ground and Further Shores of American Environmentalism [with Response]
Author: Peter A Coates
Edition/Format: Article : English
Publication: Journal of American Studies, v23 n3 (Dec., 1989): 439-446
Database: Arts & Sciences V
 
19 June 1996, Fayetteville (NC) Observer, “A park in Columbia” by Larry Cheek:
I was riding down the South Carolina highway, pondering the bumper sticker ahead of me which said, “Preserve Our Right To Arm Bears,” when signs announcing “Columbia” began appearing.
 
Animal People News
NOVEMBER 1998
CLEVELAND AMORY (1919-1998)
Cleveland Amory, 81, founder of the Fund for Animals, died in his sleep from a cerebral aneurism on October 14. Born in 1919 in Nahants, Massachusetts, and identified by the official Fund obituary as “scion of a long line of Boston merchants,” Amory was often assigned a much less blueblooded and possibly canine pedigree by the irritated targets of his wit—especially hunters, whom he argued should be hunted themselves, to prevent hunter overpopulation and to undo the effects of inbreeding.
 
“We don’t want to wipe them out,” Amory stipulated. “We only want to cull them.” His most famous slogan is memorialized by the Fund’s popular “Support your right to arm bears” bumper sticker.
 
OCLC WorldCat record
The right to arm bears
Author: Gordon R Dickson
Publisher: Riverdale, NY : Baen, ©2000.
Edition/Format: Book : Fiction : English : 1st unitary ed
 
1 June 2006, San Jose (CA) Mercury News, “Chatter Box,” pg. 2D:
Next up is a study by the group that makes ‘‘Support The Right To Arm Bears’’ bumper stickers.
   
New York (NY) Times—Dealbook 
December 8, 2008, 7:25 am  
Fleckenstein to Shutter Short-Selling Hedge Fund
By DEALBOOK
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Mr. Fleckenstein writes that he will return to a more balanced investing approach, in a vehicle that will not be a hedge fund. (His column didn’t say what would happen to some of the tchotchkes decorating his office in Seattle, including a six-foot-tall stuffed grizzly bear wearing a “Dow 10,000″ baseball cap and a sign that advises, “Protected Your Right to Arm Bears.”)
 
(Trademark)
Word Mark SUPPORT YOUR RIGHT TO ARM BEARS
Goods and Services (CANCELLED) IC 041. US 107. G & S: Charitable Services-Namely, Providing Toy Bears to Hospitalized Children and to the Elderly in Nursing Homes. FIRST USE: 19810521. FIRST USE IN COMMERCE: 19811208
Mark Drawing Code (1) TYPED DRAWING
Serial Number 73342604
Filing Date December 21, 1981
Current Basis 1A
Original Filing Basis 1A
Published for Opposition February 1, 1983
Registration Number 1235878
Registration Date April 26, 1983
Owner (REGISTRANT) Zamzow; Dale R. d.b.a. IPC INDIVIDUAL UNITED STATES P.O. Box 4610 Santa Clara CALIFORNIA 95054
Type of Mark SERVICE MARK
Register PRINCIPAL
Live/Dead Indicator DEAD
Cancellation Date September 8, 1989