In the solar wind, magnetic field power spectra usually show several power laws. In this paper, magnetic field data from the Cluster mission during an undisturbed interval of slow solar wind are analyzed at 0.28 Hz, near the spectral break point between the ion inertial and dissipation/dispersion ranges. Assuming Taylor's frozen-in condition, it corresponds to a proton kinetic scale of kvA/Ωp∼0.38, where vA and Ωp are the Alfvén speed and proton angular gyrofrequency, respectively. Data show that the Cluster spacecraft passed through a series of wave packets. A strong isolated wave packet is found to be in accordance with the four Cluster satellites crossing an Alfvén vortex, a nonlinear solution to the incompressible MHD equations. A strong agreement is seen between the data from four satellites and a model vortex with a radius of the order of 40 times the local proton gyroradii. The polarization at different spacecraft is compared and is found to agree with the vortex model, whereas it cannot be explained solely by the linear plane wave approach.