Quantifying locational carbon emissions in power grids is crucial for implementing effective carbon reduction strategies for customers relying on electricity. This paper presents a carbon-aware optimal power flow (OPF) framework that incorporates data-driven carbon tracing, enabling rapid estimation of nodal carbon emissions from electric loads. By developing generator-to-load carbon emission distribution factors through data-driven technique, the analytical formulas for both average and marginal carbon emissions can be derived and integrated seamlessly into DC OPF models as linear constraints. The proposed carbon-aware OPF model enables market operators to optimize energy dispatch while reducing greenhouse gas emissions. Simulations on IEEE test systems confirm the accuracy and computational efficiency of the proposed approach, highlighting its applicability for real-time carbon-aware system operations.