We have identified 105 galaxy pairs at z ~ 0.04 with the MaNGA integral-field spectroscopic data. The pairs have projected separations between 1 kpc and 30 kpc, and are selected to have radial velocity offsets less than 600 km/s and stellar mass ratio between 0.1 and 1. The pair fraction increases with both the physical size of the integral-field unit and the stellar mass, consistent with theoretical expectations. We provide the best-fit analytical function of the pair fraction and find that ~3% of M* galaxies are in close pairs. For both isolated galaxies and paired galaxies, active galactic nuclei (AGN) are selected using emission-line ratios and H_alpha equivalent widths measured inside apertures at a fixed physical size. We find AGNs in ~24% of the paired galaxies and binary AGNs in ~13% of the pairs. To account for the selection biases in both the pair sample and the MaNGA sample, we compare the AGN comoving volume densities with those expected from the mass- and redshift-dependent AGN fractions. We find a strong (~5x) excess of binary AGNs over random pairing and a mild (~20%) deficit of single AGNs. The binary AGN excess increases from ~2x to ~6x as the projected separation decreases from 10-30 kpc to 1-10 kpc. Our results indicate that pairing of galaxies preserves the AGN duty cycle in individual galaxies but increases the population of binary AGNs through correlated activities. We suggest tidally-induced galactic-scale shocks and AGN cross-ionization as two plausible channels to produce low-luminosity narrow-line-selected binary AGNs.