What I have is this:

What I want is to rotate the red rectangle e.g. 20 degrees, but
Sounds like you want to rotate the rect around its centerpoint.
Red rectangle is original, Yellow rectangle is rotated around the centerpoint.

To do that you need to first context.translate to the rect's centerpoint before rotating.
// move the rotation point to the center of the rect
ctx.translate( x+width/2, y+height/2 );
// rotate the rect
ctx.rotate(degrees*Math.PI/180);
Note that the context is now in its rotated state.
That means drawing position [0,0] is visually at [ x+width/2, y+height/2 ].
So you must draw the rotated rect at [ -width/2, -height/2 ] (not at the original unrotated x/y).
// draw the rect on the transformed context
// Note: after transforming [0,0] is visually [-width/2, -height/2]
// so the rect needs to be offset accordingly when drawn
ctx.rect( -width/2, -height/2, width,height);
Here is code and a Fiddle: http://jsfiddle.net/m1erickson/z4p3n/