Growing penetration of distributed energy resources connected to power distribution networks requires accurate, robust, and dependable real-Time system monitoring tools. This paper considers the state estimation (SE) problem in distribution systems and proposes a new convex relaxation based approach to solve it as a semidefinite programming problem. Even with a simple 4-bus case, we have identified that existing approaches such as the iterative Newton's method are more prone to convergence issues when measurement quality varies more significantly across different sources. By relaxing the SE problem to a convex SDP, the proposed method has the potential to closely attain the globally optimum solution without suffering from numerical issues caused by the inclusion of e.g., 'virtual measurements' at zero-injection nodes. Numerical tests have been performed on the IEEE 4-bus and 13-bus test feeder cases to demonstrate the feasibility and effectiveness of the proposed approach.