Hi! My partner has H1-B visa and he acquired this while he was still single.
And now we got married, my question is that... Can I apply for an
H4 visa or Am I qualify to apply for an H4 visa? I hope you can help me on this
I just want to clarification before going into process...

Thank you...

It doesn't matter that you're married after he already had his visa for a while or you're married long before he obtained his visa. You must be legally married and must be able to provide proof of relationship to the consulate at the interview.