We report the discovery of the first radio pulsar associated with NGC 6712, an eclipsing black widow (BW) pulsar, J1853–0842A, found by high-sensitivity searches using the Five-hundred-meter Aperture Spherical radio Telescope. This 2.15 ms pulsar is in a 3.56 hr compact circular orbit with a very low mass companion likely of mass 0.018 to 0.036 M ⊙ and exhibits eclipsing of the pulsar signal. Though the distance to PSR J1853–0842A predicted from its dispersion measure (155.125 ± 0.004 cm−3 pc) and Galactic free electron density models are about 30% smaller than that of NGC 6712 obtained from interstellar reddening measurements, this is likely due to limited knowledge about the spiral arms and Scutum stellar cloud in this direction. Follow-up timing observations spanning 445 days allow us to localize the pulsar’s position to be 0.14 core radii from the center of NGC 6712 and measure a negative spin-down rate for this pulsar of −2.39(2) × 10−21 s s−1. The latter cannot be explained without the acceleration of the globular cluster (GC) and decisively supports the association between PSR J1853–0842A and NGC 6712. Considering the maximum GC acceleration, the Galactic acceleration, and the Shklovskii effect, we place an upper limit on the intrinsic spin-down rate to be 1.11 × 10−20 s s−1. From an analysis of the eclipsing observations, we estimate the electron density of the eclipse region to be about 1.88 × 106 cm−3. We also place an upper limit of the accretion rate from the companion at about 3.05 × 10−13 M ⊙ yr−1, which is comparable with some other BWs.