Recently the small-twist-angle (< 2{\deg}) bilayer graphene has received extraordinary attentions due to its exciting physical properties. Compared with monolayer graphene, the Brillouin zone folding in twisted bilayer graphene (TBG) leads to the formation of superlattice bandgap and significant modification of density of states. However, these emerging properties have rarely been leveraged for the realization of new optoelectronic devices. Here we demonstrate the strong, gate-tunable photoresponse in mid-infrared wavelength range of 5 to 12 um. A maximum extrinsic photoresponsivity of 26 mA/W has been achieved at 12 um when the Fermi level in a 1.81{\deg} TBG is tuned to its superlattice bandgap. Moreover, the strong photoresponse critically depends on the formation of superlattice bandgap, and it vanishes in the gapless case with ultrasmall twist angle (< 0.5{\deg}). Our demonstration reveals the promising optical properties of TBG and provides an alternative material platform for tunable mid-infrared optoelectronics.