You may get cramps in your fingers when you exercise for a couple of reasons.
First, have you been drinking plenty of fluids throughout the day? Cramping can be a cause of dehydration. Be sure to stay hydrated and drink plenty of fluids throughout the day, primarily water. Avoid sugary drinks!
Second, if you are strength training, are you gripping the weights with full force? Often times individuals grip the weight more than needed. Of course you want to have a good grip on the weights to avoid losing your grip, but over-gripping may cause cramping.