What makes an artificial system a good model of intelligence? The classical test proposed by Alan Turing focuses on behavior, requiring that an artificial agent's behavior be indistinguishable from that of a human. While behavioral similarity provides a strong starting point, two systems with very different internal representations can produce the same outputs. Thus, in modeling biological intelligence, the field of NeuroAI often aims to go beyond behavioral similarity and achieve representational convergence between a model's activations and the measured activity of a biological system. This position paper argues that the standard definition of the Turing Test is incomplete for NeuroAI, and proposes a stronger framework called the ``NeuroAI Turing Test'', a benchmark that extends beyond behavior alone and \emph{additionally} requires models to produce internal neural representations that are empirically indistinguishable from those of a brain up to measured individual variability, i.e. the differences between a computational model and the brain is no more than the difference between one brain and another brain. While the brain is not necessarily the ceiling of intelligence, it remains the only universally agreed-upon example, making it a natural reference point for evaluating computational models. By proposing this framework, we aim to shift the discourse from loosely defined notions of brain inspiration to a systematic and testable standard centered on both behavior and internal representations, providing a clear benchmark for neuroscientific modeling and AI development.