Ĉar is because. Por and pro tend to mean the word 'for'. Where 'por' is is to do something in the future, and 'pro' is for something that happened in the past. Pro can be translated to because of or on account of in many cases as it would sound more natural in English. This sentence could have been I come for you, but that is less clear in the meaning.
I think of it like this. If you're standing in line to buy tickets to an event for someone, are you doing it because you are going to give them the tickets later as a gift (por), or are you doing it in place of them because they asked you to stand in place of them in the past (pro).
If you were saying, I come because you asked me too, you would be using ĉar. You're not doing this for them, rather because (a reason to).
Cxar = because
Usage example: Mi venis cxar vi demandis min veni == i came because you asked me to come
Por = for (as in meant for)
Usage example: Mi acxetis floron por vi == i bought a flower for you
Pro = for (because of)
Usage example: Mi venis pro vi == I came for you ( i came because of you )