Specify image filling color when rotating in python with PIL and setting expand argument to true

If your original image has no alpha layer, you can use an alpha layer as a mask to convert the background to white. When rotate creates the "background", it makes it fully transparent.

# original image
img = Image.open('test.png')
# converted to have an alpha layer
im2 = img.convert('RGBA')
# rotated image
rot = im2.rotate(22.2, expand=1)
# a white image same size as rotated image
fff = Image.new('RGBA', rot.size, (255,)*4)
# create a composite image using the alpha layer of rot as a mask
out = Image.composite(rot, fff, rot)
# save your work (converting back to mode='1' or whatever..)
out.convert(img.mode).save('test2.bmp')

There is a parameter fillcolor in a rotate method to specify color which will be use for expanded area:

white = (255,255,255)
pil_image.rotate(angle, PIL.Image.NEAREST, expand = 1, fillcolor = white)

https://pillow.readthedocs.io/en/stable/reference/Image.html#PIL.Image.Image.rotate

Here is a working version, inspired by the answer, but it works without opening or saving images and shows how to rotate a text.

The two images have colored background and alpha channel different from zero to show what's going on. Changing the two alpha channels from 92 to 0 will make them completely transparent.

from PIL import Image, ImageFont, ImageDraw

text = 'TEST'
font = ImageFont.truetype(r'C:\Windows\Fonts\Arial.ttf', 50)
width, height = font.getsize(text)

image1 = Image.new('RGBA', (200, 150), (0, 128, 0, 92))
draw1 = ImageDraw.Draw(image1)
draw1.text((0, 0), text=text, font=font, fill=(255, 128, 0))

image2 = Image.new('RGBA', (width, height), (0, 0, 128, 92))
draw2 = ImageDraw.Draw(image2)
draw2.text((0, 0), text=text, font=font, fill=(0, 255, 128))

image2 = image2.rotate(30, expand=1)

px, py = 10, 10
sx, sy = image2.size
image1.paste(image2, (px, py, px + sx, py + sy), image2)

image1.show()