Which one is correct?
You should know me better by now.
You should've known me better by now.

Question

Answer

The first one is right

Answer

Hi Pelin!

Depending on your context, you can use both.
Check out the example.

Your friend or special someone:
“I like you a lot, that’s the reason why i travelled all the way here to see how you’re doing.
You should know me better by now.”

You boss:
“I have a specific requirement for this job.
You should've known me better by now.  I don’t like this outcome!!

Have a great one!

Answer

You should know me better by now.