Yes. You can Google the subject for step-by-step instructions.
"Cut the sheet cane so that it is a few inches larger than the seat of the chair and soak it in warm water for several hours. Using small pieces of spline, push the sheet cane down into the groove and hold it in place in the middle of all the sides of the chair, beginning with the front. Once the sheet cane is fixed in place, use a chisel to force it into the groove of the chair, making sure that the cane stays taut at all times. When this is finished, trim the sheet cane to size using a sharp knife so that it will not poke up from the groove. Fill the groove with wood glue and tap the spline into place, wiping up excess glue as your proceed so that it does not harden."
Substitute "door frame" for "seat of the chair"

Here is a link that might be useful: Caning a Chair