Andrew has made seven appearances for the League Two leaders since signing a short-term deal in November.
"Calvin is a big, strong player and I believe we have seen glimpses of exactly what he can offer to the squad," said Vale manager Micky Adams.
"He has performed in a number of positions for us, which demonstrates his versatility, and I believe he has the ability to play an important part in our squad between now and the end of the season."
Andrew, 26, who has been used by Adams as both a striker and a winger, added: "Port Vale is a great club and I am pleased that I have the opportunity to stay at Vale Park until June.
"We have a great set of supporters and an excellent squad with a really good team spirit.
"I've enjoyed my time at the club to date and I'm certain that will continue."