Yes, a free electron at rest possesses spin. Spin is an intrinsic property of elementary particles, such as electrons. It is a quantum mechanical property that is unrelated to the classical notion of spin associated with macroscopic objects.
In quantum mechanics, particles like electrons are described by wavefunctions that contain information about their various properties, including spin. The spin of an electron can take two possible values: "up" or "down," often denoted as spin-1/2. This implies that the electron can have two distinct spin states along a particular direction.
Even when an electron is at rest, it still possesses this intrinsic spin. The spin of an electron is an inherent property that cannot be fully explained in classical terms but can be described and predicted through quantum mechanics. It plays a crucial role in determining the behavior and properties of electrons in various physical phenomena.