Yes, but they have different meanings for me.
With "how" it refers to the method; with "that" it refers to the fact.
Can you say: It's weird how/that you've asked me to be your boyfriend.
Are both okay?
I have no English teacher, I try to improve my language on my own. Thanks for your help.
If what you actually think is weird is the way, then yes. I am intrigued to know what kind of weird ways a girl or boy might use to ask someone to be her/his boyfriend.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.