Following an idea by Joyner et al. [Europhys. Lett. 107, 50004 (2014)], a microwave graph with an antiunitary symmetry T obeying T2=−1 is realized. The Kramers doublets expected for such systems are clearly identified and can be lifted by a perturbation which breaks the antiunitary symmetry. The observed spectral level spacings distribution of the Kramers doublets is in agreement with the predictions from the Gaussian symplectic ensemble expected for chaotic systems with such a symmetry.