Real Space Renormalization Group Analysis of U(1)-Gauge Theory with theta-term in 2 Dimensions

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.