Increasing emissions of greenhouse gases (GHGs) have been identified as the main contributor to global warming and climate change. Carbon dioxide (CO2) is the primary anthropogenic GHG. Carbon capture and storage (CCS) is widely recognized as a key mitigation technology that can significantly reduce CO2 emissions during combustion. It involves capturing CO2 from large stationary sources and subsequently storing it in various reservoirs such as depleted oil or gas reservoirs, saline aquifers and deep unmineable coal seams. In this work, a finite-scenario based two-stage stochastic mixed integer linear programming (MILP) model is developed for planning the retrofit of power plants with carbon capture (CC) technology and the subsequent CO2 source-sink matching in CCS supply chains under uncertainty. This model can be used to select appropriate sources, capture technologies and sinks and maximize the amount of captured and stored CO2 under the presence of uncertainty. Furthermore, to control risk at the optimal deployment of CCS systems, probabilistic financial risk metric is incorporated into the model. A case study is used to demonstrate the application of the proposed model. The computational results show that after risk management, risk of the expectation amount of captured and stored CO2 is reduced.