Stand up or sit up using straight posture. This allows you to use your abdominal muscles more efficiently to support your singing tone.
Place your hand just below your rib cage. Inhale and feel your abdomen expand. Contract your abdominal muscles gently as you exhale and hum a low tone. Visualize your tone coming from your belly, rather than your throat. The combination of visualizing and utilizing your abdominal muscles helps you produce a deeper tone.
Drop your chin and relax the muscles in your throat and face as you sing a familiar melody using low notes. Muscle relaxation is essential for producing a deeper sound.
Practice saying a breathy "ahhh" in a low voice. Add this extra bit of air to some of the notes you sing. Adding extra air to notes you hold for longer periods of time helps to produce a raspy sound.
Speak a phrase of a song, then sing it. Perform a combination of the two. Raspy singing often resembles the sound of regular speech. You have to experiment until you find a happy medium between completely speaking and completely singing, which lends your raspy vocal quality.