"It's my honor" isn't something you're likely to hear. An honor is a privilege so when somebody says "it's an honor" they mean that they are lucky to be able do it and they hold whatever it is they're talking about in high esteem. It's not quite the same though when you say "My honor" because when you say that you're talking about your own respectability, or how highly esteemed you are not so much a privilege. The word has multiple meanings, they're pretty similar but not quite the same.

Hi Mohamed - to be honest, we would never say 'it's my honour'. We would say, 'it's an honour to meet you' if we are meeting someone extraordinary. If someone says 'thank you' for something and you want to be very polite, you can say, 'it's my pleasure'. But it would be very strange English to say, 'it's my honour'. NB honour - British English; honor - American English