In project management, agility concept has emerged for overcoming the limitations of traditional methodologies that are sequential and linear. An agile project contains planned processes as well as iterations. In global competitive areas, achieving agility in outsourcing processes enables the companies to cope with changes and dynamic issues. This paper introduces an integrated cognitive map-based intuitionistic fuzzy multiple criteria decision aid to rank agile outsourcing provider alternatives and then determine the best performing one. Intuitionistic fuzzy sets are employed for dealing with uncertain and vague data along with the loss of information that may be occurred in numerical operations with fuzzy numbers. Intuitionistic fuzzy cognitive map tool is used to weight the evaluation criteria that are interrelated with each other with causal links. The most appropriate agile outsourcing provider alternative is identified via intuitionistic fuzzy complex proportional assessment technique, which aims to obtain a solution relative to the ideal solution. In order to demonstrate the robustness of the proposed intuitionistic fuzzy decision aid, a case study is conducted in Turkish white goods industry. As a comparative study, a scenario analysis is provided to understand the impacts of COVID-19 pandemic on agile provider evaluation/selection decision. According to the results obtained from the scenario analysis, it is worth noting that home office procedures are appropriate for maintaining agility in outsourcing processes of project management.