The opposite is true. A small AC current can case the heart to fibrillate and stop its normal beat, leading to death if not defibrillated to restart it. DC just causes a single contraction and then the heart can continue beating when the DC is removed (provided the current wasn't so high as to fry you otherwise). Defibrillator's do their work by applying a pulsed DC (unipolar) shock to the heart.
Tesla and Edison had a large, ongoing feud about whether AC or DC should be used for power transmission, and Edison's main argument was the DC was safer than AC. The reason AC won was because its voltage could be readily changed with transformers to allow more efficient transmission over long distances, not because it was safer.
AC current can cause continuous muscle contractions just as DC can since the muscles don't have time to relax between cycles. AC is about three times more lethal then DC for the same voltage (See
https://www.medscape.com/viewarticle/410681_3). I remember hearing of my cousin being stuck to their refrigerator door when it developed a short to the chassis and she grabbed the handle. Her mother had to pull the electrical plug so she could release her grip.
The phase of current and voltage in an AC circuit varies depending upon the type of load. For a pure resistive load the current and voltage are in phase (but of course it alternates between plus and minus voltage/current).