Short answer: No. There are no caliper mounts on the rear triangle of the frame so you can't mount brake calipers there.
There are solutions that add mount points, but they're pretty bad idea and have never taken off. Plus an adapter would probably cost more than a used bike with disks.
Most braking is done on the front wheel, so fitting a disk brake there will get you 90% of the improvements anyway. You need a disk brake rotor, disk-compatible hub, a caliper, possibly a mounting adapter, a cable or hose, and a new brake lever. Buying all that new could cost as much as a good lightly-used bike.
Your front wheel could have a disk brake - the fork has mount points on it for disk brakes. However your wheel is not disk brake compatible so you need a new hub, which probably means a replacement wheel. If you can salvage parts off another bike, then that's the only way to make it cost-effective.