This paper introduces a nonparametric test to determine whether asset return volatility follows a standard semimartingale process (with finite quadratic variation) or a rough process (with infinite quadratic variation). The test exploits the fact that rough volatility implies negatively autocorrelated increments at high frequencies, whereas semimartingale volatility yields asymptotically uncorrelated increments. The test statistic is based on the sample autocovariance of increments of spot volatility estimates, which are constructed from the empirical characteristic function of high-frequency price returns over local blocks. By choosing characteristic exponents away from zero, the method mitigates the impact of finite variation jumps, while biases from infinite variation jumps and microstructure noise are shown to have asymptotically uncorrelated increments across blocks. Under the null hypothesis of semimartingale volatility, the test statistic converges to a standard normal distribution, while under the alternative of rough volatility, it diverges to negative infinity, ensuring asymptotic power equal to one. The test is derived under very general conditions, including the presence of jumps with arbitrary activity and market microstructure noise. An empirical application to SPY high-frequency data provides strong evidence in favor of rough volatility, consistent with recent findings in the literature.