We study the gravitational wave (GW) production induced by the asymmetric jets of gamma-ray bursts (GRBs). The asymmetric jets result in a recoil force acted on the central compact object, whose motion leads to emission of GW. Under reasonable assumptions and simplifications, we derive the analytic form of the produce GWs. The amplitude of emitted GWs is estimated to be relatively low, but possibility exists that they can be detected by future experiments such as the Einstein Telescope. We find the dynamical properties of the central object, which is difficult to be studied via the electromagnetic (EW) channel, can be inferred by measuring the emitted GWs. Moreover, we find the emitted GWs can be used determine whether the relativistic jets is launched by the neutrino annihilation process or the Blandford-Znajek process, which cannot be clearly distinguished by the current GRB observations. Our work manifests the importance of the GW channel in multi-messenger astronomy. The physical information encoded in the GW and EW emissions of an astrophysical object is complementary to each other; in case some physics can not be effectively investigated using the EW channel alone, including the GW channel can be very helpful.
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