Seek out the help of your town's music commission. Each city and state has a music or arts commission that conducts business and rubs shoulders with some of the country's most popular artists. Prepare a proposal and set up a meeting with the commission.
Use social media to contact the rapper. In today's technological age, even the average Joe can make contact with today's hottest rappers, musicians, actors or sports players. With Facebook, Twitter, and YouTube, a person can simply send a direct message or push through the other thousands of people to get a one-on-one with a celebrity.
Reach out to the manager or record label. For rappers and artists, music is also a business. Many rappers conduct business through their managers or the label. Take your proposal to the label or contact them by phone. It would be wise to have your town's music commission behind you. This can make the process less of a hassle.
Raise money to hire the rapper. Rap artists make loads of money off of personal appearances alone. If your town would like to see the artist, host community events to raise money. Negotiate a price that would be acceptable to the rapper.