Yes, specific phobia can be inherited. Specific phobia runs in families, but it is not only genetic. Environmental influences can trigger specific phobia as well, which includes trauma, modeling behaviors from others, and negative information (Carandang, 2014).
Reference:
Carandang, C. (2014). Anxiety Protocol (1st ed.). Middletown, NY: Healthy Mind Research Corporation. Retrieved from http://anxietyprotocol.com/