The phrase "drag himself" is correct and can be used in written English.
For example, "He was exhausted from the long day, but he managed to drag himself out of bed and get to work on time."
Did he drag himself into the outpost?
Boris might find it a bit harder to drag himself away from the track and field!
When the policemen finally left, Yaman tried to drag himself out of the fire.
He scarcely had the energy to drag himself from the field at the end.
Brian said it was like watching a screen-saver, and tried to drag himself away.
One badly injured cat was found by his owner trying to drag himself home.
Seeking to drag himself back into the race, Bush reclaimed the mantle of the party elder.
Cornered, he could find enough of his immense fighting spirit to drag himself back into contention.
In retaliation, she stows his wheelchair in a garage and forces him to drag himself along the floor.
One evening in spring 2012 he somehow managed to drag himself home after being hit by a car.
Meanwhile Schwartzel, who doubled the opening hole, has birdied 4 and now 5 to drag himself back to level par.
