Good rappers are known for their lyrical rhymes and their recognisable voices. Some of them are blessed with deep resonating tones, while others have distinctive regional sounds. Just like vocal dialects, a rapper's voice is influenced by the people around him. Part of being a rapper is creating a distinct persona. Having a unique voice is part of that persona. Those not blessed with such a voice will have to work on making their own voice unique to the rap style.
Write down your lyrics. Though some famous rappers have notoriously not written down their lyrics, that is the exception to the rule. By writing down the lyrics it forces your brain to see the words in your mind. By visualising the words it allows your mouth to more easily form the words.
Practice your vocals. Work on getting the lyrics out clearly. Work on your timing and your flow. Being able to perform in your natural voice is more important at first than being able to sound like a rapper.
Do deep voice exercises. The sound of your voice is directly related to the throat muscles. By strengthening those muscles you will have more control over your sound. Humming along to a rap track, while lowering your tone is one exercise. Humming while displaying good posture, chest out and chin straight is another.
Do voice resonance exercises. A good rapper needs the same voice resonance as a good singer. While throat muscles are important, a strong clear voice comes from the chest. Voice resonance exercise also involves humming. Begin by humming at a comfortable pitch. Gradually shift the pitch lower, staying aware of the feeling in your chest. Increase the intensity of the humming so that you can feel the vibration. Raise the pitch until the vibration is felt both in your chest and head. Finally open your mouth while continuing to hum and increasing the intensity of the vibration. Once the vibration is felt on your lips, tongue and inside your mouth, shift the focus back to your chest. Repeat this entire exercise at least five times a day to work on strengthening your vocal resonance.
Do breathing exercises. These will not change the sound of your voice, but allow you to maintain it while rhyming over fast tracks or freestyle rapping. One breathing exercise is to bend over at the hips, so that your back is straight and try to touch your toes. Breathe slow and evenly throughout this. Another exercise is to cross your arms over your chest so that your hands are grabbing your shoulders. Breathe in and out slowly 10 times. One more exercise is to sit on the edge of a chair with your chin cupped in your hands. Place your elbows on your knees and breath slowly.
Use your personality when you rap. Exaggerate the dialect of speech in the region where you are from. Rappers are some of the originators of slang terms. The better grasp you have on the local language the more authentic you will sound.