This is a difficult question, but I'll give it my best shot. I have consulted a professor of psychology/medical doctor regarding your question, and the response I got was one of uncertainty. In the first place, the definition of a "sociopath" (i.e. person living with "antisocial personality disorder") is debatable and complex. If we must define one, generally, it is someone who is living as a the "judge of all." They have little or no conscience and they are filled with pride. They are the opposite of a modest God fearing person. From this perspective, the answer to your question would be "NO." However, there are two other considerations:
1. It has been documented that some sociopaths have become Christ-followers. Through the grace and power of God, they lead repentant and reformed lives. In this case, the answer would still be "NO."
2. A Christian becomes mentally ill and develops this condition. This person is saved by grace through faith (Ephesians 2:8-9), but for whatever reasons, he starts exhibited the symptoms of sociopathy. In this case, the answer would be "YES."
Summarily, it would appear that no matter the circumstances, the symptoms/actions belonging to a sociopath are completely incompatible with the characteristics of a Christian. Therefore, in most cases, the answer is "NO."
[Answered by Pastor HM]