The variability mechanisms from jetted active galactic nuclei (AGNs) are still under debate. Here, the damped random walk (DRW) model, implemented through Gaussian processes (GPs), is used to fit the Zwicky Transient Facility long-term optical light curves of 1684 gamma-ray emission jetted AGNs. This analysis yields one of the largest samples with characteristic optical variability timescales for jetted AGNs. A single DRW model from GPs can fit the optical light curve of most jetted AGNs well/potentially well, while there are still some jetted AGNs whose light curve cannot be fitted well by a single DRW model. After the jet power, proxied by gamma-ray luminosity, is introduced as a new parameter, new relationships among intrinsic variability time scales, black hole mass, and jet power are discovered for efficient accretion AGNs ({tau}_in_{propto}M_BH_^0.29-0.06+0.06^P_jet_^-0.3-0.03+0.03^ with scatter of approximately 0.09 dex) and for inefficient accretion AGNs ({tau}_in_{propto}M_BH_^0.06-0.07+0.07^P_jet_^0.37-0.11+0.11^ with scatter of approximately 0.14 dex), respectively. Our results support that the optical variability of jetted AGNs with efficient accretion may originate within the standard accretion disk at UV-emitting radii similar to nonjetted AGNs, and is directly related to the acceleration of shock in the jet and then enhanced through the beaming effect in beamed AGNs. For the jetted AGNs with inefficient accretion, the intrinsic timescale is consistent with the escape timescale of electrons.