My question is wheter I can say:
I am married since 3 years ago
Or I must say
I have been married for 3 years
Can they both be correct?
Correct: I have been married for three years.
You cannot say it both ways, just this way which is the perfect way to say it. To contract it, you can say " <font style="background-color: yellow;">I've</font> been married for three years."
Tim and Jack are right
I got married 3 years ago = I got married (did something once and it ended on the same day... the marriage contiuned but the act/ceremony happened in one day then it was over) so simple past tense.
I have been married for 3 years (the state of being married started started three years ago and is still continuing/still true) therefore the present perfect tense.
I have been married since [the date or year, e.g. 2014] ... also the present perfect tense.