  U(1) lattice gauge theory with $\theta$-term is investigated by real space
renormalization group approach. Flows of renormalized coupling constants are
analyzed. For each $\theta$, renormalization flows converge to a single
trajectory irrespective of bare coupling constants of real action. For $\theta
\not= \pi$ the system is in the confinement phase controlled by an infrared
fixed point. We found a phase transition at $\theta = \pi$. Imaginary part of
the action given by $\theta$-term stays fixed under renormalization group
transformations leading to deconfinement.
