In this paper, we design a new polar slotted ALOHA (PSA) protocol over the slot erasure channels, which uses polar coding to construct the identical slot pattern (SP) assembles within each active user and base station. A theoretical analysis framework for the PSA is provided... First, by using the packet-oriented operation for the overlap packets when they conflict in a slot interval, we introduce the packet-based polarization transform and prove that this transform is independent of the packet's length. Second, guided by the packet-based polarization, an SP assignment (SPA) method with the variable slot erasure probability (SEP) and a SPA method with a fixed SEP value are designed for the PSA scheme. Then, a packet-oriented successive cancellation (pSC) and a pSC list (pSCL) decoding algorithm are developed. Simultaneously, the finite-slots throughput bounds and the asymptotic throughput for the pSC algorithm are analyzed. The simulation results show that the proposed PSA scheme can achieve an improved throughput with the pSC/SCL decoding algorithm over the traditional repetition slotted ALOHA scheme. (read more)