Dear Marie, 

You are asking a general question, so I will give you a general answer, but I will add also a more particular piece of advice.  

The general question is: can a woman who has sinned seriously in the area of chastity have a conversion and become a religious?  

The general answer is, of course, yes, it is possible, just like Mary Magdalene converted and followed Jesus right up to the Cross.  

The more particular piece of advice is this: each case has to be looked at with the help of a prudent confessor or spiritual director. Between them they should examine and consider many elements, for example: the roots of the failings, their depth and number, if they have caused an addiction, the depth of the conversion, the results in a person's life (sometimes there is a rejection of men and marriage because of an abuse suffered - that would have to be healed first) etc.  

When these points are considered it may well turn out that in a particular instance the most prudent conclusion is that God is not calling that person to the celibate state.