The conformational properties of a model macromolecule, namely DNA, in an oscillatory shear flow have been investigated using Brownian dynamics (BD) simulations. To elucidate the influence of time periodic motion on the chain dynamics, the simulation results have been compared to previous experimental and BD simulation studies in steady simple shear flow. Based on these comparisons, we have determined that when the Deborah number (De), defined as the product of polymer relaxation time (lambda) and the angular forcing frequency, is less than a critical De(T), which corresponds to f(T)/2, where f(T) is the tumbling frequency of the chain in a corresponding simple steady shear flow, macromolecules exhibit similar dynamics as their steady shear flow counterpart in each half-cycle. Specifically, at De < De(T) the polymer chain experiences end-over-end tumbling events in each half-cycle, which give rise to odd harmonics in the power spectral density (PSD) of the orientation angle, where the fundamental mode of frequency corresponds to the forcing frequency f(c). At De>De(T), chain flipping is the predominant event observed. Thus there are two distinct regions in the De/De(T) parameter space: (1) a plateau regime at De/De(T)<= 1, where the chain dynamics and average conformational properties of the macromolecules are essentially the same as the corresponding steady shear flow, and (2) a power-law regime at De/De(T)>1, where the chain dimension approaches its equilibrium value as De/De(T) is significantly enhanced.