Both forms are correct. Both advisor and adviser are correct forms in English. They have the exact same meaning, which may be confusing, but there is no difference in usage or pronunciation. Advisor is slightly more common in American English and is used to describe job names. Both words are created by adding suffixes -or and -er which added to a noun give the meaning of someone doing something or working in said field. The suffixes have different origins (Latin and Germanic). The form adviser is more popular and widely used, and also a little bit older.

Definition of adviser/advisor:
noun, a person who offers advice
Every school should have a professional adviser to help students understand what are they good at.
Our sports benefit center is looking for Junior Advisor. Apply today!

Correct spelling, explanation: this form is more common as a job title in American English, but in any other field adviser wins the battle.

Correct spelling, explanation: this form is more popular in the whole English-speaking world.