The word “sorority” (from the latin soror, or “sister”) has had a long use meaning a sisterhood or a club of women. Sororities at American colleges began in 1851; several sororities were founded in the 1870s. “Sorority” meaning “a female fraternity” has been cited in print since at least 1880.
 
[This entry was assisted with research from the American Dialect Society discussion list contributors Fred Shapiro, Dan Goncharoff and Garson O’Toole.]
 
   
Wikipedia: History of North American fraternities and sororities
Sororities
The founding of the Adelphean Society (later Alpha Delta Pi) at Wesleyan Female college in 1851 marks the establishment of the first collegiate sorority. Alpha Delta Pi is one of the two “Macon Magnolias,” a term used to celebrate the bonds it shares with Phi Mu. Phi mu established at the same college was founded a year later. Alpha Delta Pi is the oldest and first secret society for women, and hosts the phrase “first, finest, forever.” In 1867, a society called I. C. Sorosis, whose motto was Pi Beta Phi was founded as a women’s fraternity at Monmouth College in Illinois (In 1888, I.C. Sorosis became known by its motto, Pi Beta Phi). It was a college fraternity from the beginning, although a few unauthorized city chapters existed for a short time in its early years. The 1870s would also host the founding of Kappa Alpha Theta in 1870, Kappa Kappa Gamma in 1870, Alpha Phi in 1872, Delta Gamma in 1873, and Gamma Phi Beta and Sigma Kappa in 1874.
 
Sororities had, from the beginning, the difficult objective of proving the viability of coeducational studies. That women could perform academically as well as or better than men while maintaining the Victorian ideals of womanhood was a tall order. Sororities created high academic standards and monitored the social activities of their members from their inception.
 
Merriam-Webster Dictionary
so·ror·i·ty noun \sə-ˈrȯr-ə-tē, -ˈrär-\
plural so·ror·i·ties
Definition of SORORITY
: a club of women; specifically : a women’s student organization formed chiefly for social purposes and having a name consisting of Greek letters
Origin of SORORITY
Medieval Latin sororitas sisterhood, from Latin soror sister
First Known Use: 1900
 
12 January 1880, Springfield (MA) Republican, “Our New York Letter,” pg. 8, col. 1:
The Fraternity club, as it is called, or as it might with more fitness be named the Fraternity and Sorority club, since it is composed of both sexes, met Wednesday evening at the house of one of the members, and the attendance was unusually large.
 
23 March 1882, The Northwestern (Northwestern University, Evanston, IL), “The Latest Arrivals,” pg. 62, cols. 1-2:
THIS school year will be memorable in the History of Woman’s College because of the advent of three ladies’ Greek letter societies. When Alpha Phi came it was greeted with surprise, creating quite a ripple among all classes.
(...)
“What warfare, bloodshed, and ruffled tempers! I tell you it will be dreadful.”
 
Our editor, to whom these remarks were addressed, froze out completely the would-be prophet with such a look as will not be soon forgotten, No sir, no such thing will ever take place at the Woman’s College. On the contrary, sorority will endeavor to improve its own members, and all will find that nothing more fortunate could have taken place than when Alpha Phi, Kappa Kappa Gamma, and Delta Gamma came to Evanston.
 
Google Books
American College Fraternities
By William Raimond Baird
New York, NY: Frank Williams
1883
Pg. 188:
GAMMA PHI BETA.
(...)
A Beta chapter was placed at the University of Michigan in 1882. The society is prosperous. The society calls itself a “Sorority” (sisterhood).
 
OCLC WorldCat record
Songs of the Gamma phi beta sorority, 1887.
Author: Gamma Phi Beta.
Publisher: [Ann Arbor, Mich., Printed by J.E. Beal, 1887]
Edition/Format:   Musical score : English
 
21 February 1891, Chicago (IL) Daily Tribune, pg. 2:
The first one of these pleasant parties was given last evening by the Kappa Kappa Gamma sorority and was attended by about 100 members and guests.
 
OCLC WorldCat record
Sorority three-step or mazurka for piano.
Author: Chas E Roat
Publisher: Battle Creek, Mich. : Chas. E. Roat Music Co., 1908.
Edition/Format:   Musical score : No Linguistic Content
 
OCLC WorldCat record
Jacquette, a sorority girl,
Author: Grace Ethelwyn Cody
Publisher: New York, Duffield, 1908.
Edition/Format:   Book : Fiction : English