The relaxation time of a viscoelastic fluid is an essential parameter for characterizing the degree of elasticity. However, measuring the relaxation time of dilute polymer solutions with low viscosity using conventional rotational rheometers remains challenging because of the low instrument sensitivity. In this study, we demonstrate an efficient microfluidic method for measuring the relaxation time of a dilute polymer solution by utilizing elasticitydriven lateral particle migration in a microchannel. First, the previous theoretical model was refined, based on the Oldroyd-B constitutive equation, in order to predict lateral particle migration in a viscoelastic fluid with constant shear viscosity, considering the inlet and finite particle size effects. This model was utilized to determine the relaxation times of dilute poly(ethylene oxide) (PEO) aqueous solutions. Direct comparison of the measured relaxation times with those obtained from Zimm theory verified the reliability of the proposed method. The current approach is expected to be useful in characterizing the relaxation times of a wide range of polymer solutions.