Const PixelMax = 32768;
Type
  pPixelArray  =  ^TPixelArray;
  TPixelArray  =  Array[0..PixelMax-1] Of TRGBTriple;

Procedure RotateBitmap_ads(
  SourceBitmap   : TBitmap;
  out DestBitmap : TBitmap;
  Center         : TPoint;
  Angle          : Double);
Var
  cosRadians          : Double;
  inX                 : Integer;
  inXOriginal         : Integer;
  inXPrime            : Integer;
  inXPrimeRotated     : Integer;
  inY                 : Integer;
  inYOriginal         : Integer;
  inYPrime            : Integer;
  inYPrimeRotated     : Integer;
  OriginalRow         : pPixelArray;
  Radians             : Double;
  RotatedRow          : pPixelArray;
  sinRadians          : Double;
begin
  DestBitmap.Width    := SourceBitmap.Width;
  DestBitmap.Height   := SourceBitmap.Height;
  DestBitmap.PixelFormat := pf24bit;
  Radians             := -(Angle) * PI / 180;
  sinRadians          := Sin(Radians);
  cosRadians          := Cos(Radians);
  For inX             := DestBitmap.Height-1 Downto 0 Do
  Begin
    RotatedRow        := DestBitmap.Scanline[inX];
    inXPrime          := 2*(inX - Center.y) + 1;
    For inY           := DestBitmap.Width-1 Downto 0 Do
    Begin
      inYPrime        := 2*(inY - Center.x) + 1;
      inYPrimeRotated := Round(inYPrime * CosRadians - inXPrime * sinRadians);
      inXPrimeRotated := Round(inYPrime * sinRadians + inXPrime * cosRadians);
      inYOriginal     := (inYPrimeRotated - 1) Div 2 + Center.x;
      inXOriginal     := (inXPrimeRotated - 1) Div 2 + Center.y;
      If
        (inYOriginal  >= 0)                    And
        (inYOriginal  <= SourceBitmap.Width-1) And
        (inXOriginal  >= 0)                    And
        (inXOriginal  <= SourceBitmap.Height-1)
      Then
      Begin
        OriginalRow   := SourceBitmap.Scanline[inXOriginal];
        RotatedRow[inY]  := OriginalRow[inYOriginal]
      End
      Else
      Begin
        RotatedRow[inY].rgbtBlue  := 255;
        RotatedRow[inY].rgbtGreen := 0;
        RotatedRow[inY].rgbtRed   := 0
      End;
    End;
  End;
End;

{Usage:}
procedure TForm1.Button1Click(Sender: TObject);
Var
  Center : TPoint;
  Bitmap : TBitmap;
begin
  Bitmap := TBitmap.Create;
  Try
    Center.y := (Image.Height  div 2)+20;
    Center.x := (Image.Width div 2)+0;
    RotateBitmap_ads(
      Image.Picture.Bitmap, 
      Bitmap, 
      Center, 
      Angle);
    Angle := Angle + 15;
    Image2.Picture.Bitmap.Assign(Bitmap);
  Finally
    Bitmap.Free;
  End;
end;