  Cubic SrTiO$_{3}$ becomes tetragonal below 105 K. The antiferrodistortive
(AFD) distortion leads to clockwise and counter-clockwise rotation of adjacent
TiO$_{6}$ octahedra. This insulator becomes a metal upon the introduction of
extremely low concentration of n-type dopants. However, signatures of the
structural phase transition in charge conduction have remained elusive.
Employing the Montgomery technique, we succeed in resolving the anisotropy of
charge conductivity induced by the AFD transition, in the presence of different
types of dopants. We find that the slight lattice distortion ($<6 \times
10^{-4}$) gives rise to a twenty percent anisotropy in charge conductivity, in
agreement with the expectations of band calculations. Application of uniaxial
strain amplifies the detectable anisotropy by disfavoring one of the three
possible tetragonal domains. In contrast with all other known anisotropic Fermi
liquids, the anisotropy has opposite signs for elastic and inelastic
scattering. Increasing the concentration of dopants leads to a drastic shift in
the temperature of the AFD transition either upward or downward. The latter
result puts strong constraints on any hypothetical role played by the AFD soft
mode in the formation of Cooper pairs and the emergence of superconductivity in
SrTiO$_3$.
