Ring polymers are a unique class of macromolecules that lack free ends and show qualitatively different dynamics compared to linear chains. Despite recent progress, the nonequilibrium flow behavior of ring polymers is not fully understood. In this work, we study ring polymer dynamics in steady shear flow using a combination of single molecule experiments and Brownian dynamics (BD) simulations. In particular, the dynamics of DNA ring polymers are studied in the flow-gradient plane of shear by using a custom flow apparatus that allows for direct observation of ring stretching and tumbling dynamics using single molecule fluorescence microscopy. Using this approach, we determined the average fractional polymer extension in the flow direction < x >/L-c and the average orientation angle with respect to the flow axis for ring polymers in dilute solution shear flow as a function of dimensionless flow strength (Weissenberg number, Wi). In all cases, results for ring polymer dynamics are directly compared to linear chain counterparts. Interestingly, our results show that rings and linear chains exhibit similar average fractional extensions, orientation angle, and dimensionless gradient thickness over a wide range of flow strengths (0 <= Wi <= 250). However, ring polymers show qualitatively different probability distributions of molecular chain extension compared to linear chains in steady shear, which arises due to the circular chain architecture that limits the conformational phase space for rings. Power spectral densities of polymer orientation angle and cross-correlations between fractional chain extension and gradient-direction thickness are used to understand ring polymer tumbling behavior, enabling determination of tumbling frequency as a function of flow strength Wi. Cross-correlations are further used to understand differences in probability distributions of molecular chain extension between linear chains and rings in shear flow. Overall, these results provide a new understanding of the nonequilibrium dynamics of ring polymers in shear flow.