Changing the origin of an image lay over the polar plot

You can use the box_alignment= to AnnotationBbox to change the reference point for the box. For instance passing box_alignment=(1,1) makes the top right corner the reference xy coordinates.

from matplotlib.offsetbox import OffsetImage, AnnotationBbox

r = np.arange(0, 2, 0.01)
theta = 2 * np.pi * r

fig = plt.figure()
ax = fig.add_subplot(111, projection='polar')
ax.plot(theta, r)
ax.set_rmax(2)
ax.set_rticks([0.5, 1, 1.5, 2])  # Less radial ticks
ax.set_rlabel_position(-22.5)  # Move radial labels away from plotted line
ax.grid(True)

img = matplotlib.image.imread("https://upload.wikimedia.org/wikipedia/en/7/7d/Lenna_%28test_image%29.png")
imagebox = OffsetImage(img, zoom=0.12)
ab = AnnotationBbox(imagebox, xy=(np.pi*225/180, 2), box_alignment=(1,1))
ax.add_artist(ab)

plt.show()

Note that you can also change the coordinate system used to place the box. For instance if you want to put your logo in the top left corner of your figure, you could do:

ab = AnnotationBbox(imagebox, xy=(0,1), xycoords='figure fraction', box_alignment=(0,1))