Yes. Kanye West can be president of the United States (whether he would become president is another question).
Kanye West will be eligible to run for president in 2020 assuming he meets the three constitutional requirements:
1. Be a natural-born citizen of the United State
Kanye Omari West was born in Atlanta, Georgia on June 8th, 1977.
2. Be at least 35 years-old
Kanye will be 42 years old in 2020.
3. Have lived in the U.S. for 15 years before running
Kanye currently resides in California and will be eligible to run as long as he doesn’t move out of the country.