<p>Rydberg atoms have stood out as a highly promising platform for realizing quantum computation. Floquet frequency modulation (FFM), in Rydberg atom systems, provides a unique tool for achieving precise quantum control and uncovering exotic physical phenomena. This work introduces a method to realize controlled arbitrary phase gates in Rydberg atoms by manipulating system dynamics using FFM. Notably, the need for laser addressing of individual atoms is eliminated, enhancing convenience for practical applications. Furthermore, this approach is integrated with soft quantum control strategies to enhance the fidelity and robustness of the resultant controlled-phase gates. Finally, as an example, this methodology is applied in Grover-Long algorithm to search target items with zero failure rate, demonstrating its substantial significance for future quantum information processing applications. This work leveraging Rydberg atoms and FFM may herald a new era of scalable and reliable quantum computing.</p>