I've had a hoarse voice for a few months. Other symptoms: heartburn, throat clearing, sore throat. I am 29 and a smoker. Throat cancer?

Wouldn't . Automatically jump to that conclusion. Would encourage you to have your throat evaluated by your physician or an ENT specialist.However you aren't doing yourself any favors with the continued tobacco use. Strongly encourage you to quit.
Hoarseness can be. Caused by many conditions that produce inflammation of the vocal folds including infection, allergies, gerd(acid reflux), voice overuse, breathing/ingesting irritating substances, heavy smoking ; cancers of the pharynx (throat), larynx, thyroid or lung. Smoking is a major risk factor for developing throat cancers, but it is unusual at age 29. See a doctor for evaluation ; help quitting smoking.