We introduce a possible disruption mechanism of dust grains in planet formation by their spinning motion. This mechanism has been discussed as rotational disruption for the interstellar dust grains. We theoretically calculate whether porous dust aggregates can be disrupted by their spinning motion and if it prohibits dust growth in protoplanetary disks. We assume radiative torque and gas-flow torque as driving sources of the spinning motion, assume that dust aggregates reach a steady-state rigid rotation, and compare the obtained tensile stress due to the centrifugal force with their tensile strength. We model the irregularly-shaped dust aggregates by introducing a parameter, $gamma_mathrm{ft}$, that mimics the conversion efficiency from force to torque. As a result, we find that porous dust aggregates are rotationally disrupted by their spinning motion induced by gas flow when their mass is larger than $sim10^8$ g and their volume filling factor is smaller than $sim 0.01$ in our fiducial model, while relatively compact dust aggregates with volume filling factor more than 0.01 do not face this problem. If we assume the dust porosity evolution, we find that dust aggregates whose Stokes number is $sim0.1$ can be rotationally disrupted in their growth and compression process. Our results suggest that the growth of dust aggregates may be halted due to rotational disruption or that other compression mechanisms are needed to avoid it. We also note that dust aggregates are not rotationally disrupted when $gamma_mathrm{ft}leq0.02$ in our fiducial model and the modeling of irregularly-shaped dust aggregates is essential in future work.
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