Neutrino magnetic moment ($ u$MM) is an important property of massive neutrinos. The recent anomalous excess at few keV electronic recoils observed by the Xenon1T collaboration might indicate a $sim 2.2times10^{-11} mu_B$ effective neutrino magnetic moment ($mu_ u^{eff}$) from solar neutrinos. Therefore, it is essential to carry out the $ u$MM searches at a different experiment to confirm or exclude such hypothesis. We study the feasibility of doing $ u$MM measurement with 4 kton active mass at Jinping neutrino experiment using electron recoil data from both natural and artificial neutrino sources. The sensitivity of $mu_ u^{eff}$ can reach $1.2times10^{-11}mu_B$ at 90% C.L. with 10-year data taking of solar neutrinos. Besides the intrinsic low energy background $^{14}$C in the liquid scintillator, we find the sensitivity to $ u$MM is highly correlated with the systematic uncertainties of $pp$ and $^{85}$Kr. Reducing systematic uncertainties ($pp$ and $^{85}$Kr) and the intrinsic background ($^{14}$C and $^{85}$Kr) can help to improve sensitivities below these levels and reach the region of astrophysical interest. With a 3 mega-Curie (MCi) artificial neutrino source $^{51}$Cr installed at Jinping neutrino detector for 55 days, it could give us a sensitivity to the electron neutrino magnetic moment ($mu_{ u_e}$) with $1.1times10^{-11} mu_B$ at 90% C.L.. With the combination of those two measurements, the flavor structure of the neutrino magnetic moment can be also probed at Jinping.
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