How can I correct my drooping shoulders?

There are a number of reasons why shoulders droop. It could be due to incorrect posture, weak upper back muscles, the habit of stooping because you are too tall, etc. You can do the following exercises particularly for the upper back BUT you must also workout the rest of the body so that there is stability and balance in your self:

Push-ups

Rowing for the muscles in the upper back

Upright rows for the muscles in the shoulders

Shoulder press for the deltoids