You can have a romantic relationship with someone with Asperger’s every bit as much as you can with anyone else—your expectations going into the relationship may just require some refining.
People with Asperger’s Syndrome tend to be very literal thinkers who adhere to the logic of saying what they mean, and meaning what they say. If you are someone with a laissez faire attitude about honoring commitments; or if you tend to be less than punctual when meeting dates and appointments, this could be problematic as the person with Asperger’s may take it very personally as a sign that you are uncaring.
People with Asperger’s also tend to be “pleasers” for desiring to be socially accepted, and may agree to participate in social or community events as a knee-jerk reaction to wanting to do what you want to do. You may then find yourself disappointed or confused at your partner's disengagement during the activity. Most all “Aspergians” have acute sensory sensitivities that can make some social activities (fireworks, rock concerts, crowded environments) extremely painful and overwhelming.
Also know that people with Asperger’s—in saying what they mean—can be very frank and honest. So be prepared if you ask your partner a hypothetical question such as, “Does this outfit make me look fat?” because you may not like the answer you hear.
Finally, people with Asperger’s usually need solitary time and space, and may become very preoccupied with a passionate topic of interest to the point where you may feel overlooked or neglected. If you share a common interest with your romantic partner, there will be an incentive to create mutually-pleasing activities together.