Atomic receivers based on Rydberg vapor cells as sensors of electromagnetic fields offer a promising alternative to conventional radio frequency front-ends. In multi-antenna configurations, the magnitude-only, phase-insensitive measurements produced by atomic receivers pose challenges for traditional detection methods. Existing solutions rely on two-step iterative optimization processes, which suffer from cascaded channel estimation errors and high computational complexity. We propose a channel state information (CSI)-free symbol detection method based on in-context learning (ICL), which directly maps pilot-response pairs to data symbol predictions without explicit channel estimation. Simulation results show that ICL achieves competitive accuracy with {higher computational efficiency} compared to existing solutions.