Select the camera with right-click (or left-click whichever is you select button)
Reset the location of the camera to the origin with alt + g
Reset the rotation of the camera to zero with alt + r
Open the options panel with n
Set the camera’s x rotation to 90 degrees
Move the camera back along the y-axis with g then y, pull the camera back in front of Suzzane until Suzzane is in frame. You can check this by pressing 0 on your numpad.
Create an empty with shift + a –> Empty –> Plain axes
Scale the plain axes with s so that they are bigger than Suzzane
Parent the camera to the plain axes by selecting the camera then shift + selecting the plain axes. Then press ctrl + p –> object.
We need three keyframes of the plain axes so select just the plain axes.
Set the first keyframe in front of Suzzane with i –> Rotation. Make sure your mouse is in the 3D viewport.
Go to frame 20 on the dopesheet. Set the rotation of the plain axes along the z axis to 180 degrees. Set the keyframe again with i –> Rotation.
Go to frame 40 on the dopesheet. Set the rotation of the plain axes along the z axis to 360 degrees. Set the keyframe once again with i –> Rotation.
Set the end frame for the animation to 40.
To make the animation smooth, hover over the timeline and press t then select linear.