Hey. Girlfriend of an Aspie here, and NT myself.
Omg! Yes! It can happen! Apparently.
The answer is...YES, Aspies can get girlfriends. Boyfriends too, if they're that way inclined.
I have discovered though, that there is a HUGE area that lets most Aspie guys down. The focus is on 'I want a girlfriend' rather than 'I want to be in a relationship'. A girlfriend is not a posession! She is your 'other half'...she is expected to give to you, but YOU most be prepared to GIVE TO HER.
Relationships are reciprocal...it is all about balance. As much as you need her presence, support and affection, you need to give her the same. You need to be there for her. You can't take take take and never give.
When she cries, you must offer her at least some sympathy. A silent hug is good!
When she's happy, you should celebrate with her.
When she's confused or lost, try to help her find her way.
When she's sad or hurt, make it better.
When she's lonely, why the hell are you not there? She shouldn't be!
It's just like...when you need a helping hand, she has two spare.
When you're feeling down, she's there to make it less painful.
When you're angry, she's there to listen to you rant and rave.
When you just want to feel someone's presence in the room, there she is.
When you feel like having a good time...ditto.
If you're ready to GIVE in a relationship as well as receive, then you're ready for a girlfriend.
Also, the other half of the major brickwall syndrome...are you tasty? Are you delicious? Are you simply scrumptious? Or are you a little smelly, little old-looking, scruffy and generally distasteful?
Sure, you need to find a girl that loves you for who you are. But what girl in their right mind is even going to CONSIDER a guy that smells like a men's gym, looks like a wolverine, dresses like a 12 year old and speaks in all tongues of depressed?
Find the spruced-up you inside, put him on display. Say you're carrot-cake-flavoured. It's comfortable sitting around, fresh out of the tin, no icing, still with little bits of tinfoil sticking out of you. That's you, that's comfortable. But uh...would you sell that to random customers? NO. You want to put some icing on there...nothing over the top, just something that looks nice. Shave off the little burnt bits and pull out the excess tinfoil. If you feel like going all-out, put a bit of garnish on top. Meh girls will just nibble the garnish off and be on their way... WOW girls will stop by, like what they see, take a bite and realise what an EXCELLENT cake it is. They'll want the whole lot to themselves!
So. If you want a girlfriend,
a) Remember it's about her as much as it's about you. Prepared to do a whole lot of revelling in the rewards of having your very own female? Dude...you sure as hell better be ready to give as well as you receive.
b) Represent yourself appropriately. Women go for the 'best they can get', and often go for guys that seem just a step or two 'above their social tier'. If you look like you don't give a damn about the way you look, don't be surprised if the best offers you get are random old fat ladies or mad cat lady next door. Make yourself tasty and tempting enough for your TARGET girls...offer carrots, you'll get rabbits. Offer worms, you'll get birds.