  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 indices ranging
from $-0.7$ to $-3.6$. 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, with some significant outliers likely resulting
from frequency channel resolution limits outside of this range. We derive
interstellar scattering-based transverse velocities assuming a scattering
screen halfway between the pulsar and earth. We also calculate 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 were
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 ns or less.
