Stochastic optimization methods have gained significant prominence as effective techniques in contemporary research, addressing complex optimization challenges efficiently. This paper introduces the Parrot Optimizer (PO), an efficient optimization method inspired by key behaviors observed in trained Pyrrhura Molinae parrots. The study features qualitative analysis and comprehensive experiments to showcase the distinct characteristics of the Parrot Optimizer in handling various optimization problems. Performance evaluation involves benchmarking the proposed PO on 35 functions, encompassing classical cases and problems from the IEEE CEC 2022 test sets, and comparing it with eight popular algorithms. The results vividly highlight the competitive advantages of the PO in terms of its exploratory and exploitative traits. Furthermore, parameter sensitivity experiments explore the adaptability of the proposed PO under varying configurations. The developed PO demonstrates effectiveness and superiority when applied to engineering design problems. To further extend the assessment to real-world applications, we included the application of PO to disease diagnosis and medical image segmentation problems, which are highly relevant and significant in the medical field. In conclusion, the findings substantiate that the PO is a promising and competitive algorithm, surpassing some existing algorithms in the literature. The supplementary files and open-source codes of the proposed parrot optimizer (PO) is available at https://aliasgharheidari.com/PO.html.