Can one become a nun if one was married in the Church but divorced civilly?
After an annulment is granted, some orders may accept that individual - others will not.
Some orders would accept a divorced woman with a decree of nullity, some would not. Some orders accept widows, some only accept the never married. Of course, minor children would be an impediment. The only way to know is to ask the order.
As others have stated you would need an annulment. You may be able to become an Oblate or an Associate with some communities. You would need to be debt free and if you have dependents, they would need to come of age and be independent of you in order to enter a community. Yes, it is possible, but be sure that it is what you want.
I’ve heard of couples in Church history that entered a convent (i.e. husband to one convent, wife to another) after raising their children, with mutual consent and without annulment. 1 Kor 7:5.