Polycyclic aromatic hydrocarbon (PAH) emission has long been proposed to be a potential star formation rate indicator, as it arises from the photodissociation region bordering the Stromgren sphere of young, massive stars. We apply a recently developed technique of mid-infrared spectral decomposition to obtain a uniform set of PAH measurements from Spitzer low-resolution spectra of a large sample of star-forming galaxies spanning a wide range in stellar mass (M_*_~10^6^-10^11.4^M_{sun}_) and star formation rate (~0.1-2000M_{sun}_/yr). High-resolution spectra are also analyzed to measure [NeII]12.8{mu}m and [NeIII]15.6{mu}m, which effectively trace the Lyman continuum. We present a new relation between PAH luminosity and star formation rate based on the [NeII] and [NeIII] lines. Calibrations are given for the integrated 5-15{mu}m PAH emission, the individual features at 6.2, 7.7, 8.6, and 11.3{mu}m, as well as several mid- infrared bandpasses sensitive to PAH. We confirm that PAH emission is suppressed in low-mass dwarf galaxies, and we discuss the possible physical origin of this effect.