We present a galaxy classification system for 238 (E1-Sdm) CALIFA (Calar Alto Legacy Integral Field Area) galaxies based on the shapes and amplitudes of their circular velocity curves (CVCs). We infer the CVCs from the de-projected surface brightness of the galaxies, after scaling by a constant mass-to-light ratio based on stellar dynamics - solving axisymmetric Jeans equations via fitting the second velocity moment V_{rms}=√{V^2+σ ^2} of the stellar kinematics. We use principal component analysis (PCA) applied to the CVC shapes to find characteristic features and use a k-means classifier to separate circular curves into classes. This objective classification method identifies four different classes, which we name slow-rising (SR), flat (FL), round-peaked (RP) and sharp-peaked (SP) circular curves. SR are typical for low-mass, late-type (Sb-Sdm), young, faint, metal-poor and disc-dominated galaxies. SP are typical for high-mass, early-type (E1-E7), old, bright, metal-rich and bulge-dominated galaxies. FL and RP appear presented by galaxies with intermediate mass, age, luminosity, metallicity, bulge-to-disc ratio and morphologies (E4-S0a, Sa-Sbc). The discrepancy mass factor, fd = 1 - M*/Mdyn, have the largest value for SR and SP classes (˜ 74 per cent and ˜ 71 per cent, respectively) in contrast to the FL and RP classes (with ˜ 59 per cent and ˜ 61 per cent, respectively). Circular curve classification presents an alternative to typical morphological classification and appears more tightly linked to galaxy evolution.