To improve power efficiency in vehicle-to-roadside infrastructure (V2I) communication networks, this paper proposes a joint power and sub-carrier assignment policy under delay aware quality of service (QoS) requirements. Due to the real-time nature of the V2I transmissions, the proposed policy should satisfy delay aware QoS requirements with a minimized power consumption. In particular, we develop a cross-layer framework in which orthogonal frequency division multiplexing (OFDM) is employed at the physical layer and the proposed power and sub-carrier assignment policy works at the data link layer. Under the assumption that the instantaneous channel state information (CSI) of all users is known, the optimization problem can be formulated and solved with the help of a time-sharing factor. The obtained results show that both the optimal power allocation and the optimal sub-carrier assignment depend on the delay aware QoS requirements of each user. We also theoretically prove that the proposed power allocation policy converges to the classical water-filling policy if we do not consider the QoS requirements. Experimental results reveal that the proposed policy offers a superior performance over the existing resource allocation policies.