While it is tempting to believe that data distillation preserves privacy, distilled data's empirical robustness against known attacks does not imply a provable privacy guarantee. Here, we develop a provably privacy-preserving data distillation algorithm, called differentially private kernel inducing points (DP-KIP). DP-KIP is an instantiation of DP-SGD on kernel ridge regression (KRR). Following a recent work, we use neural tangent kernels and minimize the KRR loss to estimate the distilled datapoints (i.e., kernel inducing points). We provide a computationally efficient JAX implementation of DP-KIP, which we test on several popular image and tabular datasets to show its efficacy in data distillation with differential privacy guarantees.