Of course, provided he meets all the other regular admission requirements to the priesthood, namely that he is a practising Catholic, is still capable of completing the necessary formation, and there are no impediments, and that a bishop or a religious congregation is willing to take him.
I personally know a man who after many years of marriage, had a number of children, and after his wife passed away, was accepted to the priesthood. The confusing part is of course that his children and grandchildren also live in the area. Some unsuspecting visitors to the parish were in for a ride when they find this priests being called Dad and Grandpa by a group of people.
Besides widower, sometimes divorcee can be admitted to the priesthood as well. This one is a bit more complicated. The man needs to have the marriage annulled.
And that he was not the culprit of the failed marriage or under warning from the annulment declaration.