Technically the answer is "yes". There are seminarians like Blessed John XXIII Seminary in Boston which specialize in delayed vocations for men who have children.
I think it depends on:
- the diocese that you apply to, and
- the age of your children.
I very much doubt you would be accepted if you had children still dependent upon you.
Of course, one's marital status is a factor as well. I would think that most of these priest's wives have died, but that isn't always the case.
Finally, don't forget the call to the permanent diaconate —
- Are you sure that God is not leading you in that direction?