From my Urban Dictionary
Text Out: To weasel out of a prior engagement by text message. Not to be confused with text message breakup. Alternative meaning: The action of asking someone to be your boyfriend/girlfriend by texting them instead of asking in person or over the phone.
Man, I can't bear the thought of going to dinner with Jane again, so I think I am going to text out.
I was recently asked to serve on a committee by text and gave the person asking a hard time. I guess I'm old fashioned but I like to be asked in person...Dude, I heard you're goin out with Sarah. When did you ask her out?
Oh I texted her last night
Man, dude you texted her out? That's lame.