Yes, you can. BUT that is entirely up to the discretion of the Passport Agency.
If I Have A Felony , Can I Get A Passport?
The answer is yes. It is possible to get a passport with a warrant out for your arrest. As long as your name isn't in the central name check system you will be fine. The only why your name would be in this system is if a request is put in by law enforcement. So if you for example Killed someone and are running then it's a bad idea but for a warrant lets say for probation violation you will be fine.
Yes you can get a passport but you may be denied a passport if you are facing a trial and have an outstanding warrant. The procedure of getting a passport for a convicted felon is the exact the same way as it is for anyone else. But some countries do not allow convicted felons to enter, even after they get a U.S. Passport. www.expresspassport.com