Of all the non-allopathic (CAM – complementary and alternative) therapies out there, the only one that has been systematically studied is accupuncture.
Puncturing of the Neiguan, Shenmen and Xinshu spots has been advocated to treat atrial fibrillation.
The best study I can find in a peer reviewed journal is from JCE 2011. 80 patients post cardioversion of atrial fibrillation were randomized to accupuncture, sham accupuncture or amiodarone. Accupuncture reduced recurrence of atrial fibrillation. This needs to be studied further before making firm recommendations.
Accupuncture likely works by autonomic modulation of the vagus nerve.
Lombardi et. al. have a well written article re. accupuncture.
Liu et.al. have done a meta-analysis on accupuncture for cardiac arrhythmias – atrial fibrillation and ventricular premature beats (VPB or PVC).