iRotationAxis, jRotationAxis is the center of rotation.
You can speed this up a lot by creating an array of scanlines for the input and output bitmaps before calling the procedure, then replace the Scanline calls in the procedure with an assignment to the array entry.

[delphi]type
TRGBTripleArray = ARRAY[0..MaxPixelCount-1] OF TRGBTriple;
pRGBTripleArray = ^TRGBTripleArray;

procedure RotateBitmap(CONST BitmapOriginal: TBitmap;
VAR BitmapOut : TBitmap;
CONST iRotationAxis, jRotationAxis: INTEGER;
CONST AngleOfRotation: DOUBLE {radians} );
VAR
cosTheta : EXTENDED;
i : INTEGER;
iOriginal : INTEGER;
iPrime : INTEGER;
j : INTEGER;
jOriginal : INTEGER;
jPrime : INTEGER;
RowOriginal: pRGBTripleArray;
RowRotated : pRGBTRipleArray;
sinTheta : EXTENDED;
BEGIN
// Get SIN and COS in single call from math library
sincos(AngleOfRotation, sinTheta, cosTheta);

// Step through each row of rotated image.
FOR j := BitmapOut.Height-1 DOWNTO 0 DO
BEGIN
RowRotated := BitmapOut.Scanline[j];
jPrime := j - jRotationAxis;

FOR i := BitmapOut.Width-1 DOWNTO 0 DO
BEGIN
iPrime := i - iRotationAxis;
iOriginal := iRotationAxis + ROUND(iPrime * CosTheta - jPrime * sinTheta);
jOriginal := jRotationAxis + ROUND(iPrime * sinTheta + jPrime * cosTheta);

// Make sure (iOriginal, jOriginal) is in BitmapOriginal. If not,
// assign blue color to corner points.
IF (iOriginal >= 0) AND (iOriginal = 0) AND (jOriginal