You can. It's hard, but you can. My husband and I have been together for six years, he has aspergers, and I don't. I totally know where you're coming from. Any relationship has its trials, but we seem to have more sometimes! If you ever want to talk, feel free to send me a PM. It can work, it just takes a little more work. It's beyond worth it though.
I try to remind myself of how he interprets the world, and understand his point of view. It's very different from mine, and putting myself in his shoes when I don't understand his actions truly does help. Especially when it comes to some of his sensory issues, or social situations that overwhelm him, taking that time to look at the world from his angle helps me help him. If you've never read any of her books, you should look into Temple Grandin's writing. She's very good at explaining how her mind works, and it really helped me understand how he thinks.
I'm sure reading around here will help too 