You would not be prohibited from applying and receiving a liquor license in Arkansas with a misdemeanor on your record. You will need to apply for the license through the Alcoholic Beverage Control Administration Division. Their website is: http://www.arkansas.gov/dfa/abc_administration/abcadm_index.html
Arkansas requires that those applying for a liquor license be free of felony convictions, that their location has the ability to seat at least 50 people at one time, and that you meet certain financial requirements.
Before you apply, you need to determine which category you fall under, since Arkansas has several categories of liquor licenses. The licenses aren't the same, but rather are based on the type of business operated. For example, those opening a restaurant inside a motel fall under a different category than those operating a private club or a liquor store.
To apply, you will need to ask for an application from the ABC office in Little Rock. In some situations, you may be able to have the application sent to you if you live a significant distance away from the office. Otherwise, request an application from the head office. The contact info is listed on the link I provided above.
Once you get your application, you will need to complete it using all information required by the state of Arkansas, and include any other information they need. You'll probably need to include a copy of your state ID such as a driver's license, and you may need to undergo a background or fingerprint check.