We present a detailed study of the pulsation of alpha Circini, the brightest of the rapidly oscillating Ap stars. We have obtained 84 days of high-precision photometry from four runs with the star tracker on the WIRE satellite. Simultaneously, we collected ground-based Johnson B observations on 16 nights at the South African Astronomical Observatory. In addition to the dominant oscillation mode at 2442 microHz, we detect two new modes that lie symmetrically around the principal mode to form a triplet. The average separation between these modes is 30.173+-0.004 microHz and they are nearly equidistant with the separations differing by only 3.9 nHz. We compare the observed frequencies with theoretical pulsation models based on constraints from the recently determined interferometric radius and effective temperature, and the recently updated Hipparcos parallax. We show that the theoretical large separations for models of alpha Cir with global parameters within the 1-sigma observational uncertainties vary between 59 and 65 microHz. This is consistent with the large separation being twice the observed value, indicating that the three main modes are of alternating even and odd degrees. The frequency differences in the triplet are significantly smaller than those predicted from our models, for all possible combinations of mode degrees, and may indicate that the effects of magnetic perturbations need to be taken into account. The WIRE light curves are modulated by a double wave with a period of 4.479 days, and a peak-to-peak amplitude of 4 mmag. This variation is due to the rotation of the star and is a new discovery, made possible by the high precision of the WIRE photometry. The rotational modulation confirms an earlier indirect determination of the rotation period.
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