Today the term "circle" is being claimed by neopagan, social, and political groups to describe their members in a specific place or those addressing a particular topic. One even appears to include a gifting pyramid style scam.
A work dated ca. 1917, 'The Beautiful Ministry of Womanhood: A Survey of the Opportunities for Ministries of Kindness for Christian Womanhood, Including Social Service Circle programs." by Dean C. Dutton, Ph.D. was published by The Great Life Publishing Company, Kansas City, Missouri. It sold for fifteen cents and was only 33 pages softbound.
Trying to locate information on the Social Service Circle, the following was found:
"In 1912, Dr. Joshua Stansfield, minister of Meridian Street Methodist Church, formed a committee to be a link between the church and social service work of the city. It was called the Social Service Circle. Aid was given in various ways - support to French war orphans, milk money to School #12, college money loans to deserving, but needy students, and the purchase of everything from false teeth to sewing machines and steel chairs." (http://www.stansfieldcircle.org/index_files/Page570.htm)
Avenues of Faith: Shaping the Urban Religious Culture of Richmond, Virginia ... By Samuel C. Shepherd Jr. provides more clues that at about this same time a new emphasis was beginning to spread to enlarge the traditional spiritual focus of church work into improving the social setting of people and addressing the needs and issues surrounding illness, poverty, greed, and violence. The church had to be involved in a "new Pentecost" and understand that the church could not act or exist separate from bettering the life of others in society. This emphasis on a "community redemption" emerged in the late 1880's and was often known as "social gospel." (University of Alabama Press 2001; pg. 138-148).
In most churches surveyed, and with what little information could be found on the women's groups origins in them, apparently women often formed into mission driven groups and under this umbrella smaller groups devoted to a specific cause (orphans) or skill (quilting) might form in larger churches or communities. Some larger early churches might have as many as a dozen smaller groups (or circles) functioning under the banner of that women's mission group.
One example is the United Methodist Women (who formed in 1972 as a single entity bringing together all the diverse women's groups of the denominations that had united in 1938 and 1968) of the new United Methodist Church.
Local UMW group
---> Circle for Quilting women
---> Circle for women working outside the home
---> Circle for Stay at home Moms