What was the first women's college in the USA?

Both Wesleyan College in Macon, GA and Mount Holyoke College in South Hadley, MA claim this distinction.

''...the first college in the world chartered to grant degrees to women in 1836,''
https://www.wesleyancollege.edu/about/Index.cfm

''Founded in 1837 by chemist and revolutionary educator Mary Lyon, Mount Holyoke is the nation's oldest continuing institution of higher learning for women. It was the first of the Seven Sisters, the female equivalent of the formerly all-male Ivy League.''
http://www.mtholyoke.edu/cic/about/facts.shtml

1894 - The Annex is chartered as Radcliffe College by the Commonwealth of Massachusetts.
http://www.radcliffe.edu/about/sig.html

Wesleyan College
http://www.wesleyancollege.edu/

You are probably referring to Georgia Female College, which opened its doors in 1839. It was later renamed Wesleyan College.

Mount Holyoke College was founded in 1837, and was originally named Mount Holyoke Female Seminary.

https://en.wikipedia.org/wiki/Timeline_of_women%27s_colleges_in_the_United_States