  We present a measurement of the rate of type Ia supernovae (SNe Ia) from the
first of three seasons of data from the SDSS-II Supernova Survey. For this
measurement, we include 17 SNe Ia at redshift $z\le0.12$. Assuming a flat
cosmology with $\Omega_m = 0.3=1-\Omega_\Lambda$, we find a volumetric SN Ia
rate of $[2.93^{+0.17}_{-0.04}({\rm systematic})^{+0.90}_{-0.71}({\rm
statistical})] \times 10^{-5} {\rm SNe} {\rm Mpc}^{-3} h_{70}^3 {\rm
year}^{-1}$, at a volume-weighted mean redshift of 0.09. This result is
consistent with previous measurements of the SN Ia rate in a similar redshift
range. The systematic errors are well controlled, resulting in the most precise
measurement of the SN Ia rate in this redshift range. We use a maximum
likelihood method to fit SN rate models to the SDSS-II Supernova Survey data in
combination with other rate measurements, thereby constraining models for the
redshift-evolution of the SN Ia rate. Fitting the combined data to a simple
power-law evolution of the volumetric SN Ia rate, $r_V \propto (1+z)^{\beta}$,
we obtain a value of $\beta = 1.5 \pm 0.6$, i.e. the SN Ia rate is determined
to be an increasing function of redshift at the $\sim 2.5 \sigma$ level.
Fitting the results to a model in which the volumetric SN rate,
$r_V=A\rho(t)+B\dot \rho(t)$, where $\rho(t)$ is the stellar mass density and
$\dot \rho(t)$ is the star formation rate, we find $A = (2.8 \pm 1.2) \times
10^{-14} \mathrm{SNe} \mathrm{M}_{\sun}^{-1} \mathrm{year}^{-1}$, $B =
(9.3^{+3.4}_{-3.1})\times 10^{-4} \mathrm{SNe} \mathrm{M}_{\sun}^{-1}$.
