What's the difference of meaning between those sentences?
I sent her a text asking her if she wants to go to see a movie together this weekend.

I sent her a text asking her if she wanted to go to see a movie together this weekend.

What's the difference of meaning between those sentences?

Question

What's the difference of meaning between those sentences?
I sent her a text asking her if she wants to go to see a movie together this weekend.

I sent her a text asking her if she wanted to go to see a movie together this weekend.

What's the difference of meaning between those sentences?

Answer

Both are perfect, but.. 
if you use 'wants', it seems that the situation is still ongoing - she hasn't replied yet, maybe..
if you use 'wanted', I expect you to tell me the result:   '... but she said she's busy today.'
:)

Answer

"Wants" is present tense and "Wanted" is past tense. As "sent" is already in past tense I believe only the second sentence is gramatically correct.