Yes, its safety used as a food additive has been approved by the U.S. Food and Drug Administration (FDA), European Food Safety Authority (EFSA),  Joint FAO/WHO Expert Committee on Food Additives (JECFA), as well as other authorities.

FDA
It is generally recognized as safe (GRAS) when used in accordance with good manufacturing practices in food and feed. (3) (4)

It can be used as an antimicrobial agent, antioxidant, color or coloring adjunct, curing or pickling agent, flavor enhancer, flavoring agent or adjuvant. (5)

EFSA

Erythorbic acid (E 315) is listed in Commission Regulation (EU) No 231/2012 as an authorised food additive in the EU as “Additives other than colours and sweeteners”. (6)

http://www.chinafooding.com/Erythorbic_Acid