  Recently, several regional pulsar timing array collaborations, including
CPTA, EPTA, PPTA, and NANOGrav, have individually reported compelling evidence
for a stochastic signal at nanohertz frequencies. This signal originates
potentially from scalar-induced gravitational waves associated with significant
primordial curvature perturbations on small scales. In this letter, we employ
data from the EPTA DR2, PPTA DR3, and NANOGrav 15-year data set, to explore the
speed of scalar-induced gravitational waves using a comprehensive Bayesian
analysis. Our results suggest that, to be consistent with pulsar timing array
observations, the speed of scalar-induced gravitational waves should be $c_g
\gtrsim 0.61$ at a $95\%$ credible interval for a lognormal power spectrum of
curvature perturbations. Additionally, this constraint aligns with the
prediction of general relativity that $c_g=1$ within a $90\%$ credible
interval. Our findings underscore the capacity of pulsar timing arrays as a
powerful tool for probing the speed of scalar-induced gravitational waves.
