We extract interstellar scintillation parameters for pulsars observed by the NANOGrav radio pulsar timing program. Dynamic spectra for the observing epochs of each pulsar were used to obtain estimates of scintillation timescales, scintillation bandwidths, and the corresponding scattering delays using a stretching algorithm to account for frequency-dependent scaling. We were able to measure scintillation bandwidths for 28 pulsars at 1500 MHz and 15 pulsars at 820 MHz. We examine scaling behavior for 17 pulsars and find power-law indices ranging from −0.7 to −3.6, though these may be biased shallow due to insufficient frequency resolution at lower frequencies. We were also able to measure scintillation timescales for six pulsars at 1500 MHz and seven pulsars at 820 MHz. There is fair agreement between our scattering delay measurements and electron-density model predictions for most pulsars. We derive interstellar scattering-based transverse velocities assuming isotropic scattering and a scattering screen halfway between the pulsar and Earth. We also estimate the location of the scattering screens assuming proper motion and interstellar scattering-derived transverse velocities are equal. We find no correlations between variations in scattering delay and either variations in dispersion measure or flux density. For most pulsars for which scattering delays are measurable, we find that time-of-arrival uncertainties for a given epoch are larger than our scattering delay measurements, indicating that variable scattering delays are currently subdominant in our overall noise budget but are important for achieving precisions of tens of nanoseconds or less.