This question came up in a recent Bible study. We were covering the book of Romans, the last few verses of chapter 2. Circumcision came up. After a little discussion, a sister in Christ asked how women made a covenant with God under Mosaic Law, since circumcision was the sign of the covenant. How were women "circumcised" before Christ?
The circumcision did not make the covenant. The covenant was made between Abraham and God with the sacrifice of animals (Genesis 15) and it applied to all of Abraham's descendants. Circumcision was the sign of the covenant or the witness or reminder that the covenant existed. "And you shall be circumcised in the flesh of your foreskins, and it shall be a sign of the covenant between Me and you" (Genesis 17:11). While a refusal to have the witness marked in his flesh would exclude an Israelite male (Genesis 17:14), it does not mean every Israelite had to carry the witness -- in this case it was only required of the males.
For example, the sign of the covenant with Noah is the rainbow (Genesis 9:12-17). I don't have to see a rainbow for that covenant to be in place. In fact, God worded it that the rainbow was a reminder for Him and not us.
Under the new law baptism becomes the sign of the covenant (Colossians 2:11-12). Baptism does not create the covenant, that was created when Jesus died on the cross (Hebrews 9:15). Baptism is our witness or reminder that we are under Christ's covenant. One of the differences between the Old Covenant and the New Covenant is that everyone who becomes a Christian is required to take on this sign, whether male or female.