Being one of the key derivatives of phasor measurement units (PMUs), a synchrophasor-only linear state estimator (LSE) presents a reliable, high quality, and truly dynamic picture of the power grid. However, with the increase in number of buses monitored by PMUs, computational burden will become a critical constraint for the state estimation solver. Although installing additional hardware can be a possible solution, such a solution will considerably raise the cost of capital investment, operation, and maintenance. This paper proposes cloud-computing as a cost-effective alternative to the computational burden problem. This paper also presents feasibility of the cloud based solution with regards to scalability of the system and latency incurred. Our solution is designed to address the critical operational parameters such as latency and variable network sizes. Additionally, the LSE application establishes robust communication procedures to process inputs arriving at high data rates from multiple PMUs. The paper concludes by highlighting future research directions for enhancing such cloud based solutions.