It's fairly easy to hang a curtain inside a door casing. Hardware manufacturers make sockets that are intended for use on the insides of window frames, and they work equally well on door frames. If you can measure accurately and use a screwdriver, you can have your sockets up and your curtain hung in about five minutes. If you don't want to mar your woodwork, try using a tension rod instead.
Measure the inside width of your doorframe. Purchase a straight, pole-type curtain rod in the exact width and two inside-mount sockets that will accept the rod. Or purchase a tension rod that will fit the doorway.
Measure the header on your curtain (the fabric that rises above the curtain rod).
Measure from the top of the left side of the doorframe to a point equal to the height of the header and mark it. Repeat on the right side of the doorframe.
Attach the inside-mount sockets, if you're using a pole rod. Place a socket, with its top edge on the mark you made, on the left side of the doorframe and screw it into the frame. Repeat for the right side. Slide the curtain onto the rod and set the rod in the brackets.
Slide your curtain onto the tension rod, if this is your choice. Place the tension rod on the marks you made and twist it counter-clockwise to tighten it against the doorframe.