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The recently released data by pulsar timing array (PTA) collaborationspresent strong evidence for a stochastic signal consistent with agravitational-wave background. Assuming this signal originates fromscalar-induced gravitational waves, we jointly use the PTA data from theNANOGrav 15-yr data set, PPTA DR3, and EPTA DR2 to probe the small-scalenon-Gaussianity. We put the first-ever constraint on the non-Gaussianityparameter, finding $|F_\mathrm{NL}|\lesssim 13.9$ for a lognormal powerspectrum of the curvature perturbations. Furthermore, we obtain $-13.9 \lesssimF_\mathrm{NL}\lesssim -0.1$ to prevent excessive production of primordial blackholes. Moreover, the multi-band observations with the space-bornegravitational-wave detectors, such as LISA/Taiji/TianQin, will provide acomplementary investigation of primordial non-Gaussianity. Our findings pavethe way to constrain inflation models with PTA data.

Implications for the non-Gaussianity of curvature perturbation from pulsar timing arrays