  We present predictions for the the K^- \alpha scattering length obtained
within the framework of the multiple scattering approach. Evaluating the pole
position of the K^- \alpha scattering amplitude within the zero range
approximation, we find a loosely bound K^- \alpha state with a binding energy
of E_R = -2 ... -7 MeV and a width \Gamma_R = 11 ... 18 MeV. We propose to
measure the K^- \alpha scattering length through the final state interaction
between the \alpha and K^- meson produced in the reaction dd \to \alpha K^+
K^-. It is found that the K^-\alpha invariant mass distribution from this
reaction at energies near the threshold provides a new tool to determine the
s-wave K^- \alpha scattering length.
