procedure RotateBitmap(Bitmap: TBitmap; Angle: Double; BackColor: TColor);
type TRGB = record
B, G, R: Byte;
end;
pRGB = ^TRGB;
pByteArray = ^TByteArray;
TByteArray = array[0..32767] of Byte;
TRectList = array [1..4] of TPoint;

var x, y, W, H, v1, v2: Integer;
Dest, Src: pRGB;
VertArray: array of pByteArray;
Bmp: TBitmap;

procedure SinCos(AngleRad: Double; var ASin, ACos: Double);
begin
ASin := Sin(AngleRad);
ACos := Cos(AngleRad);
end;

function RotateRect(const Rect: TRect; const Center: TPoint; Angle: Double): TRectList;
var DX, DY: Integer;
SinAng, CosAng: Double;
function RotPoint(PX, PY: Integer): TPoint;
begin
DX := PX - Center.x;
DY := PY - Center.y;
Result.x := Center.x + Round(DX * CosAng - DY * SinAng);
Result.y := Center.y + Round(DX * SinAng + DY * CosAng);
end;
begin
SinCos(Angle * (Pi / 180), SinAng, CosAng);
Result[1] := RotPoint(Rect.Left, Rect.Top);
Result[2] := RotPoint(Rect.Right, Rect.Top);
Result[3] := RotPoint(Rect.Right, Rect.Bottom);
Result[4] := RotPoint(Rect.Left, Rect.Bottom);
end;

function Min(A, B: Integer): Integer;
begin
if A < B then Result := A
else Result := B;
end;

function Max(A, B: Integer): Integer;
begin
if A > B then Result := A
else Result := B;
end;

function GetRLLimit(const RL: TRectList): TRect;
begin
Result.Left := Min(Min(RL[1].x, RL[2].x), Min(RL[3].x, RL[4].x));
Result.Top := Min(Min(RL[1].y, RL[2].y), Min(RL[3].y, RL[4].y));
Result.Right := Max(Max(RL[1].x, RL[2].x), Max(RL[3].x, RL[4].x));
Result.Bottom := Max(Max(RL[1].y, RL[2].y), Max(RL[3].y, RL[4].y));
end;

procedure Rotate;
var x, y, xr, yr, yp: Integer;
ACos, ASin: Double;
Lim: TRect;
begin
W := Bmp.Width;
H := Bmp.Height;
SinCos(-Angle * Pi/180, ASin, ACos);
Lim := GetRLLimit(RotateRect(Rect(0, 0, Bmp.Width, Bmp.Height), Point(0, 0), Angle));
Bitmap.Width := Lim.Right - Lim.Left;
Bitmap.Height := Lim.Bottom - Lim.Top;
Bitmap.Canvas.Brush.Color := BackColor;
Bitmap.Canvas.FillRect(Rect(0, 0, Bitmap.Width, Bitmap.Height));
for y := 0 to Bitmap.Height - 1 do begin
Dest := Bitmap.ScanLine[y];
yp := y + Lim.Top;
for x := 0 to Bitmap.Width - 1 do begin
xr := Round(((x + Lim.Left) * ACos) - (yp * ASin));
yr := Round(((x + Lim.Left) * ASin) + (yp * ACos));
if (xr > -1) and (xr < W) and (yr > -1) and (yr < H) then begin
Src := Bmp.ScanLine[yr];
Inc(Src, xr);
Dest^ := Src^;
end;
Inc(Dest);
end;
end;
end;

begin
Bitmap.PixelFormat := pf24Bit;
Bmp := TBitmap.Create;
try
Bmp.Assign(Bitmap);
W := Bitmap.Width - 1;
H := Bitmap.Height - 1;
if Frac(Angle) <> 0.0
then Rotate
else
case Trunc(Angle) of
-360, 0, 360, 720: Exit;
90, 270: begin
Bitmap.Width := H + 1;
Bitmap.Height := W + 1;
SetLength(VertArray, H + 1);
v1 := 0;
v2 := 0;
if Angle = 90.0 then v1 := H
else v2 := W;
for y := 0 to H do VertArray[y] := Bmp.ScanLine[Abs(v1 - y)];
for x := 0 to W do begin
Dest := Bitmap.ScanLine[x];
for y := 0 to H do begin
v1 := Abs(v2 - x)*3;
with Dest^ do begin
B := VertArray[y, v1];
G := VertArray[y, v1+1];
R := VertArray[y, v1+2];
end;
Inc(Dest);
end;
end
end;
180: begin
for y := 0 to H do begin
Dest := Bitmap.ScanLine[y];
Src := Bmp.ScanLine[H - y];
Inc(Src, W);
for x := 0 to W do begin
Dest^ := Src^;
Dec(Src);
Inc(Dest);
end;
end;
end;
else Rotate;
end;
finally
Bmp.Free;
end;
end;

// Использование
RotateBitmap(Image1.Picture.Bitmap, StrToInt(Edit1.Text), clWhite);