No, platinum does not turn yellow.
Platinum is a naturally white metal and is highly resistant to chemical reactions, meaning it will not tarnish or corrode.
The yellowing that people often associate with white jewelry is actually a problem with white gold, which is made from yellow gold mixed with white alloys and then coated with a rhodium plating. When the rhodium plating wears off of white gold, the natural yellow tint of the gold underneath becomes visible.
Platinum does not require this plating, so it remains its natural white color forever. Instead of yellowing, it develops a soft, velvety surface known as a patina (from micro-scratches), which gives it a slightly dull or frosted look over time, but this can be polished back to its original high shine.