Debris disks and asteroid belts are expected to form around young pulsars due to fallback material from their original supernova explosions. Disk material may migrate inwards and interact with a pulsar's magnetosphere, causing changes in torque and emission. Long term monitoring of PSR J0738-4042 reveals both effects. The pulse shape changes multiple times between 1988 and 2012. The torque, inferred via the derivative of the rotational period, changes abruptly from September 2005. This change is accompanied by an emergent radio component that drifts with respect to the rest of the pulse. No known intrinsic pulsar processes can explain these timing and radio emission signatures. The data lead us to postulate that we are witnessing an encounter with an asteroid or in-falling debris from a disk.