Can I petition for my dad who has a criminal record?

You can petition for your father regardless of his criminal record, because the petition only establishes the family relationship. However, he may be found inadmissible to the U.S. if he has multiple convictions (not just arrests) when he applies for an immigrant visa at the U.S. consulate.

Your father's criminal past will be a factor if he wants to return to the US. You must consult with an experienced immigration attorney and who has to see and review the entirety of your father's criminal and immigration history. Although, some criminal criminal convictions and even some immigration infractions will result in an almost permanent bar from ever returning to the US, some convictions or violations on the other hand only prescribe temporal bars, and in those cases, there is forgiveness called waivers, which are usually based upon showing of hardship to qualifying US relatives of the alien who will be affected if waiver is not granted for the alien to return to the United States. In other to make a determination of your father's immigration options, it is crucial (at least for me) to carefully review his entire file.

Your question requires an attorney consultation. It is not a simple question that can be answered on this type of forum. There are many factors that would need to be considered and evaluated. Depending on exactly what those charges were and whether or not he was convicted, he can be deemed inadmissible and will be unable to return to the U.S.

The best thing to do would be to gather his complete criminal record for all arrests, charges, convictions, etc., and let an attorney review those documents. The reason is that some convictions, especially drug-related, could possibly create a bar (even a permanent bar) from re-entering the U.S. You should know for sure before you take the time and spend the money to file for him.