High-performance Host processors can integrate Processing-In-Memory (PIM) devices, which can accelerate memory-intensive kernels of Machine Learning (ML) models, including Large Language Models (LLMs), by leveraging the large memory bandwidth available at PIM cores. However, Host processor needs consecutive elements distributed across DRAM banks, while PIM cores need consecutive elements within their local banks. This necessitates data rearrangements in ML kernel execution that pose significant performance and programmability challenges, further exacerbated by the need to support diverse PIM devices. Current compilation approaches lack systematic optimization for diverse ML kernels and multiple PIM devices, and may largely ignore data rearrangement costs during the compute code optimization step. We show that data rearrangements and compute code optimization are interdependent, and need to be jointly optimized during the tuning process. Therefore, we design DCC, the first data-centric ML compiler for PIM systems that jointly co-optimizes data rearrangements and compute code in a unified tuning process. DCC integrates a multi-layer PIM abstraction to support multiple PIM backends. DCC enables effective co-optimization of data partitioning strategies with compute loop partitioning schemes. DCC applies PIM-specific code optimizations, and leverages a fast and accurate performance prediction model to select the bestperforming code schedule for a given kernel on a target PIM architecture. Our evaluations in various individual ML kernels show that DCC achieves up to 7.68x speedup (2.21x average) on HBM-PIM, and up to 13.17x speedup (3.92x average) on AttAcc PIM, over GPU-only execution. In end-to-end LLM inference, DCC on AttAcc accelerates GPT-3 and LLaMA-2 by 4.52x average (up to 7.71x in LLaMA-2) over GPU. DCC is open-sourced at https://github.com/SPIN-Research-Group/DCC.