Can I use 14 AWG pigtails on a 20 amp 12 AWG circuit with 15 amp receptacles?
You must use a 12 gauge pigtail here

A 14 gauge pigtail on a 20A circuit is a (very short) tap conductor:


  Tap Conductors. As used in this article, a tap conductor is
  defined as a conductor, other than a service conductor, that
  has overcurrent protection ahead of its point of supply that
  exceeds the value permitted for similar conductors that are
  protected as described elsewhere in 240.4.


As a result, that 14AWG pigtail violates NEC 210.19(A)(4) Exception 1, which prohibits the use of tap conductors to feed receptacles:


  (4) Other Loads. Branch-circuit conductors that supply
  loads other than those specified in 210.2 and other than
  cooking appliances as covered in 210.19(A)(3) shall have
  an ampacity sufficient for the loads served and shall not be
  smaller than 14 AWG.
  
  Exception No.1: Tap conductors shall have an ampacity sufficient for 
  the load served. In addition, they shall have
  an ampacity of not less than 15 for circuits rated less
  than 40 amperes and not less than 20 for circuits rated
  at 40 or 50 amperes and only where these tap conductors
  supply any of the following loads:
  
  (a) lndividual lampholders or luminaires with taps extending not longer than 450 mm (18 in.) beyond any portion of the lampholder or luminaire.
  
  (b) A luminaire having tap conductors as provided in
  410.117.
  
  (c) Individual outlets, other than receptacle outlets,
  with taps not over 450 mm (18 in.) long.
  
  (d) Infrared lamp industrial heating appliances.
  
  (e) Nonheating leads of deicing and snow-melting
  cables and mats.