We demonstrate the use of propagating spin waves for implementing a reservoir-computing architecture. Our concept utilizes an active-ring resonator comprising a magnetic thin-film delay line with an integrated feedback loop. These systems exhibit strong nonlinearity and delayed response, two important properties required for an effective reservoir-computing implementation. In a simple design, we exploit the electric control of feedback gain to inject input data into the active-ring resonator and use a microwave diode to read out the amplitude of the spin waves circulating in the ring. We employ two baseline tasks, namely the short-term memory and parity-check tasks, to evaluate the suitability of this architecture for processing time-series data.