General-purpose vision-language models offer a promising way to zero-shot robot control: \gptastra{} excels at open-ended and language- or image-conditioned manipulation but remains substantially weaker on high-precision and long-horizon tasks. We introduce \emph{RoboICL}, an in-context robot-control framework that narrows these gaps without robot-specific parameter updates or a learned VLA. RoboICL separates \emph{demonstration context}, which provides recorded examples when available, from \emph{interaction memory}, which accumulates the model's own actions and observed outcomes. Both use a shared observation--action--receipt--observation grammar. To preserve experience across task stages, RoboICL combines sampled demonstration blocks with bounded anchored memory. Fixed anchors keep earlier rollout interactions available for in-context learning, while the latest interaction supports immediate error correction. Across 30 RoboDojo tasks, using zero shot for Open and one demonstration elsewhere, RoboICL improves on official zero-shot \gptastra{} by 20--27 progress-score points in every category. It leads the leaderboard baselines on Memory and Open, achieves comparable performance to the strongest Precision baseline, and remains competitive on Long-Horizon. Its 30-task Overall score is 50.64, versus 33.68 for the strongest baseline. On a separate ten-task subset, RoboICL scores 60.60, within 2.00 points of the $π_{0.5}$ + \gptastra{} hybrid approach. On three real-robot tasks, mean progress rises from 14.45 at zero shot to 63.33 at one shot and 78.89 at three shots. On two development tasks, optional Jev-gated action reuse reduces \gptastra{} calls by 33--48\%. Code is available at \href{https://github.com/Mosi-AI/RoboICL}{https://github.com/Mosi-AI/RoboICL}.

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