The PandaX-4T liquid xenon detector at the China Jinping Underground Laboratory is used to measure the solar ^{8}B neutrino flux by detecting neutrinos through coherent scattering with xenon nuclei. Data samples requiring the coincidence of scintillation and ionization signals (paired), as well as unpaired ionization-only signals (US2), are selected with energy threshold of approximately 1.1 keV (0.33 keV) nuclear recoil energy. Combining the commissioning run and the first science run of PandaX-4T, a total exposure of 1.20 and 1.04 tonne·year are collected for the paired and US2, respectively. After unblinding, 3 and 332 events are observed with an expectation of 2.8±0.5 and 251±32 background events, for the paired and US2 data, respectively. A combined analysis yields a best-fit ^{8}B neutrino signal of 3.5 (75) events from the paired (US2) data sample, with ∼37% uncertainty, and the background-only hypothesis is disfavored at 2.64σ significance. This gives a solar ^{8}B neutrino flux of (8.4±3.1)×10^{6} cm^{-2} s^{-1}, consistent with the standard solar model prediction. It is also the first indication of solar ^{8}B neutrino "fog" in a dark matter direct detection experiment.