Is it possible for a divorced Catholic to become a priest?
It is possible, however it is not probable. For starters, the man is still considered married by the Church until an investigation by a marriage tribunal finds the marriage to be null. There is no canonical impediment to a man who has an annulment becoming a priest however the issue of scandal presents itself in such situations. The local community may be hurt and confused and divided over such a situation and bishops are sensitive to such issues. So while there is no definitive block to the path of ordination for such a man, there is a practical reality that must be dealt with. Some dioceses just outright refuse to consider such men for ordination, other dioceses will consider such men after a set period of time following the annulment, and other dioceses consider such men on a case by case basis.