A number of the saints had terrible pasts before their conversions. Thus, your past doesn’t necessarily preclude your being a priest provided you have no impediments as mentioned in the previous reply.
I would hasten to add a couple comments. If your past is terribly murky and dark, be sure to thoroughly discern what you may feel right now is your calling. You want to be sure you have conquered all your sins and desires of the past because Satan is going to really attack you with remembrances and desires of those past sins when you are a priest. Sins of the flesh and homosexuality are the ones that have the strongest effect and, thus, take the longest to discern they have been conquered. For the sake of Jesus, His church and your soul you don’t want to end up like a good number of priests who have caused great harm and scandal to themselves and others by falling back into their pasts.
Secondly, through your discernment period and during all the rest of your life as a priest (if you indeed become a priest), bring out ALL your past into the light – no matter how shameful it would be to you, those close to you and to those who don’t know you. This serves three purposes: 1) setting you free from the past by shining the light of full truth on it; 2) showing others the example of the loving providence and complete mercy of God towards ALL sinners, and; 3) keeping you free from trying to hide your past and thus potentially walking down the dark road of lies.
Pray mightily to the Holy Spirit during these next months – or even years – of discernment and He will tell you LOUD AND CLEAR what your vocation in life is to be – priest or no priest. I’ll be praying for you.