  The recently released data by pulsar timing array (PTA) collaborations
present strong evidence for a stochastic signal consistent with a
gravitational-wave background. Assuming this signal originates from
scalar-induced gravitational waves, we jointly use the PTA data from the
NANOGrav 15-yr data set, PPTA DR3, and EPTA DR2 to probe the small-scale
non-Gaussianity. We put the first-ever constraint on the non-Gaussianity
parameter, finding $|F_\mathrm{NL}|\lesssim 13.9$ for a lognormal power
spectrum of the curvature perturbations. Furthermore, we obtain $-13.9 \lesssim
F_\mathrm{NL}\lesssim -0.1$ to prevent excessive production of primordial black
holes. Moreover, the multi-band observations with the space-borne
gravitational-wave detectors, such as LISA/Taiji/TianQin, will provide a
complementary investigation of primordial non-Gaussianity. Our findings pave
the way to constrain inflation models with PTA data.
