While AI coding tools have demonstrated potential to accelerate software development, their use in scientific computing raises critical questions about code quality and scientific validity. In this paper, we provide ten practical rules for AI-assisted coding that balance leveraging capabilities of AI with maintaining scientific and methodological rigor. We address how AI can be leveraged strategically throughout the development cycle with four key themes: problem preparation and understanding, managing context and interaction, testing and validation, and code quality assurance and iterative improvement. These principles serve to emphasize maintaining human agency in coding decisions, establishing robust validation procedures, and preserving the domain expertise essential for methodologically sound research. These rules are intended to help researchers harness AI's transformative potential for faster software development while ensuring that their code meets the standards of reliability, reproducibility, and scientific validity that research integrity demands.