  We study the derived categories of twisted supersingular K3 surfaces. We
prove a derived crystalline Torelli theorem for twisted supersingular K3
surfaces, characterizing Fourier-Mukai equivalences in terms of isomorphisms
between their associated K3 crystals. This is a positive characteristic analog
of the Hodge-theoretic derived Torelli theorem of Orlov, and its extension to
twisted K3 surfaces by Huybrechts and Stellari. We give applications to various
questions concerning Fourier-Mukai partners, extending results of
C\u{a}ld\u{a}raru and Huybrechts and Stellari. We also give an exact formula
for the number of twisted Fourier-Mukai partners of a twisted supersingular K3
surface.
