Do you need a commercial rating for aerial application work?
Short answer: you can do aerial application on your own crops with a private certificate, but if you're going to do it commercially then you need a commercial certificate. In both cases you also need an agricultural aircraft operator certificate.



An agricultural aircraft operator certificate is required for aerial application, per 14 CFR 137.11. The airman certification requirements are in 137.19:


  (b) Private operator—pilot. The applicant must hold a current U.S.
  private, commercial, or airline transport pilot certificate and be
  properly rated for the aircraft to be used.
  
  (c) Commercial operator—pilots. The applicant must have available the
  services of at least one person who holds a current U.S. commercial or
  airline transport pilot certificate and who is properly rated for the
  aircraft to be used.


The FAA's AC 137, Certification Process for Agricultural Aircraft Operators has all the details about how to get an operator's certificate and the airman requirements are in section 2-3. It says:


  Pilots designated to conduct operations for the commercial operator
  applicant must hold a current commercial or airline transport pilot
  certificate with the appropriate ratings


A private operator is limited to working his own crops:


  Private agricultural aircraft operators may not conduct operations for
  compensation or hire, or conduct operations over a congested area. The
  operator must provide proof of property ownership or other property
  interest in the crop located on that property where the operation will
  be conducted.


By the way, there's no such thing as a "commercial rating" in the US; private and commercial are both certificates.