I want to change my current 15 amp split outlet to a 20 amp Can I use a pigtail on the red and black ( at both ends) to do this?
No you cannot do this.  The reason it's a 15A circuit is that it's wired with 14 ga. wire.  For a 20A circuit it generally takes 12 ga. wire.  So just changing out the plug does nothing but create a dangerous situation.

If you need a 20A GFCI-protected circuit the best and correct approach is to pull a new 12 ga. wire from a new GFCI breaker in the panel.