In OFDM-based optical networks, multiple subcarriers can be allocated to accommodate various size of traffic demands. By using the multi-carrier modulation technique, subcarriers for the same node-pair can be overlapping in the spectrum domain. Compared to the traditional wavelength routed networks (WRNs), the OFDM-based Spectrum-sliced Elastic Optical Path (SLICE) network has higher spectrum efficiency due to its finer granularity and frequency-resource saving. In this work, for the first time, we comprehensively study the routing and spectrum allocation (RSA) problem in the SLICE network. After proving the NP-hardness of the static RSA problem, we formulate the RSA problem using the Integer Linear Programming (ILP) formulations to optimally minimize the maximum number of sub-carriers required on any fiber of a SLICE network. We then analyze the lower/upper bounds for the sub-carrier number in a network with general or specific topology. We also propose two efficient algorithms, namely, balanced load spectrum allocation (BLSA) algorithm and shortest path with maximum spectrum reuse (SPSR) algorithm to minimize the required sub-carrier number in a SLICE network. The results show that the proposed algorithms can match the analysis and approximate the optimal solutions using the ILP model.