This paper addresses the limitations of classical correlation measures when data are imprecise, inherently vague, or affected by measurement uncertainty. We develop a new method for computing the correlation coefficient and conducting the corresponding hypothesis test for intuitionistic fuzzy data. Using the  $(alpha, beta)$-cut approach and formulating an associated nonlinear programming problem, we derive the intuitionistic fuzzy correlation coefficient and generalize the related test statistic. We demonstrate the effectiveness of the method through two numerical examples and an extensive simulation study across three uncertainty levels and various sample sizes. Simulation results indicate that under high uncertainty, the proposed method substantially reduces the Type I error rate and achieves higher power than the approach based on conventional fuzzy sets. Furthermore, by enabling separate modeling of membership and non-membership degrees, the proposed method allows for evaluating the distinct influence of each component on the final outcomes, leading to more realistic analyses in imprecise environments.