  $TeO_2$ crystals are used as bolometers in experiments searching for Double
Beta Decay without emission of neutrinos. One of the most important issues in
this extremely delicate kind of experiments is the characterization of the
background. The knowledge of the response to $\alpha$ particles in the energy
range where the signal is expected is therefore a must. In this paper we report
the results on the response function of a $TeO_2$ bolometer to $\alpha$'s
emitted by $^{147}$Sm dissolved in the crystal at the growth phase. A Quenching
Factor of ($1.0076\pm 0.0005$) is found, independent of the temperature in the
investigated range. The energy resolution on $\alpha$ peaks shows a standard
calorimeter energy dependence: $\sigma\; [\rm{keV}] = (0.56 \pm 0.02) \oplus
(0.010 \pm 0.002)\sqrt{E[\rm{keV}]} $. Signal pulses show no difference between
$\alpha$ and $\beta\gamma$ particles
