I twisted my knee in bed. I propped it up while I slept and when I woke up that thigh was stiff and I'm noticing a bit of swelling. Is that normal?

Inflammation. Anything that can cause a twist or pop in many joints can cause irritation leading to the inflammatory response. This response includes pain and swelling which can make joints stiff. This is normal for the inflammatory process though should be examined if developing (including/not limited to) catching, locking, giving way, significant worsening of pain, fevers, weakness/numbness.