To squeeze. Examples 1400–1895, N.E.D.

1

1817.  Winding his body round both the tiger and the tree [the serpent] girted both with all his violence, till the ribs and other bones began to give way.—Mass. Spy, Oct. 29: from the South Carolina Telescope.

2

1830.  The chest girted in [by a corset] till breath can scarcely be drawn.—Id., Sept. 15: from the Medico-Chirurgical Review.

3