The optical light curve of the quasar PG 1302-102 at $z = 0.278$ shows a strong, smooth 5.2 yr periodic signal, detectable over a period of $sim 20$ yr. Although the interpretation of this phenomenon is still uncertain, the most plausible mechanisms involve a binary system of two supermassive black holes with a subparsec separation. At this close separation, the nuclear black holes in PG 1302-102 will likely merge within $sim 10^{5}$ yr due to gravitational wave emission alone. Here we report the rest-frame near-infrared time lags for PG 1302-102. Compiling data from {it WISE} and {it Akari}, we confirm that the periodic behavior reported in the optical light curve from Graham et al. (2015) is reproduced at infrared wavelengths, with best-fit observed-frame 3.4 and $4.6 mu$m time lags of $(2219 pm 153, 2408 pm 148)$ days for a near face-on orientation of the torus, or $(4103pm 153, 4292 pm 148)$ days for an inclined system with relativistic Doppler boosting in effect. The periodicity in the infrared light curves and the light-travel time of the accretion disk photons to reach the dust glowing regions support that a source within the accretion disk is responsible for the optical variability of PG 1302-102, echoed at the further out dusty regions. The implied distance of this dusty, assumed toroidal region is $sim$ 1.5 pc for a near face-on geometry, or $sim$1.1 pc for the relativistic Doppler boosted case.