Charlie Sheen to Farrah Abraham -- Hell Yeah, I'll Go On a Date!

Farrah Abraham is involved in a full on textual relationship with Charlie Sheen, TMZ has learned -- and the two are now planning to hook up in person.

TMZ has obtained text messages that show the "Backdoor Teen Mom" porn star first reached out to Sheen back in May saying she hopes to meet Sheen if she can score herself a role on "Anger Management."

Farrah even took the initiative ... and asked Sheen out on a date -- either a parent playdate with their kids ... or an adult get together for some coffee.

Sheen's response: "Coffee is for amateurs and grandma."

He also said he's down to meet up ... because ... well, he's probably a big fan of her work.

Farrah followed up with Sheen and asked him to an event she would be attending with some "porn star ppl" ... but Sheen wasn't able to attend.

We're told they have stayed in touch ... and are trying to work out a date to see each other ASAP, but they're both busy with work ... and kids ... and porn.

Stay tuned ...