An earth-boring rotary drill bit includes a bit body configured to carry one or more cutters for engaging a subterranean earth formation, the bit body comprising a particle-matrix composite material having a plurality of hard particles dispersed throughout a matrix material, the matrix material comprising a shape memory alloy. The matrix material comprises a metal alloy configured to undergo a reversible phase transformation between an austenitic phase and a martensitic phase. The matrix material may include an Ni-based alloy, Cu-based alloy, Co-based alloy, Fe-based alloy or Ti-based alloy. The drill bit may be made by a method that includes: providing a plurality of hard particles in a mold to define a particle precursor of the bit body; infiltrating the particle precursor of the bit body with a molten matrix material comprising a shape memory alloy forming a particle-matrix mixture; and cooling the molten particle-matrix mixture to solidify the matrix material and forming a bit body having a particle-matrix composite material comprising a shape memory alloy.