My sister and I were having a conversation and I joked about her relationship status without knowing that people were already pestering her about it, so she got mad and because I was an easy target she pointed her anger on me, so I got mad as well and talked back. Now she's really mad and talks about me having no respect on her.

It's frustrating. What should I do?

Let her cool down and then apologize

If you had something to say about a relationship she has, and it upset her, then you are automatically in the wrong. It's her relationship! Now you know to not joke about it.
"Just joking" doesn't cut it. When you apologize, don't make any excuses.

Even though you likely just meant it as sisterly teasing, and meant no harm by it, because it did obviously upset her, the onus is on you to let her know that you're sorry for teasing her; that you didn't mean to upset her.