What is the prayer of faith as recorded in James 5:15? James 5:15 says that the prayer of faith will save the sick. Is there a specific prayer of faith?
The verse is not referring to any specific prayer, but rather to the prayer of faith (ευχη της πιστεως) as opposed to prayer that is undertaken without faith.  For this reason James emphasizes a verse later:


  The entreaty of a righteous man hath much strength


He further provides Elijah as an example (v.17-18):


  Elijah was a man subject to like passions as we are, and he prayed earnestly that it might not rain: and it rained not on the earth by
  the space of three years and six months. And he prayed again, and the
  heaven gave rain, and the earth brought forth her fruit.