  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
1.25 and 1.04 tonne$\cdot$year are collected for the paired and US2,
respectively. After unblinding, 3 and 332 events are observed with an
expectation of 2.8$\pm$0.5 and 251$\pm$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 $\sim$37\%
uncertainty, and the background-only hypothesis is disfavored at 2.64$\sigma$
significance. This gives a solar $^8$B neutrino flux of
($8.4\pm3.1$)$\times$10$^6$ cm$^{-2}$s$^{-1}$, consistent with the standard
solar model prediction. This is the first indication of solar $^8$B neutrino
``fog'' in a dark matter direct detection experiment.
