We propose a Yang-Mills field theory of gravity based on a unitary phase gauge invariance of the Lagrangian where the gauge transformations are those of the SU(2)\ifmmode\times\else\texttimes\fi{}U(1) symmetry of the two spinors. In a classical limit this microscopic theory results in Einstein's metrical theory of gravity, where we restrict ourselves in a first step to its linearized version. Furthermore, only the case of massless particles is treated explicitly.