Does "Ego Peccator" mean "I'm Sinner"? I used many web translation services but I'm still not sure.
Google Translate is notoriously bad with Latin, and to my knowledge others aren't much better. Therefore it is always good to ask a Latinist, so I'm glad you found your way to our site instead of relying on online translators.
Ego means "I" and peccator means "sinner". In Latin the verb "to be" can be omitted when clear from context, but it is still implicitly there. That is, ego [sum] peccator means "I [am] a sinner". The translation you have is indeed a valid one, whether the original has sum or not.
If there is another verb, then the sum is often no longer implicitly there. Context, be it from other sentences or from this one being a part of a longer sentence, can change the meaning. I only discussed the phrase in isolation.