  A non-supersymmetric renormalizable $SO(10)$ model, with CP invariant Yukawa
sector consisting of Lorentz scalars in $10$ and $\overline{126}$ dimensional
representations, is proposed. The elemental Yukawa couplings are real due to CP
symmetry. The latter is broken in the low energy effective theory through the
standard model Higgs which is a complex linear combination of electroweak
doublets residing in $10$ and $\overline{126}$ scalars. As a result, the mass
matrices in the quark and lepton sectors, including those of heavy and light
neutrinos, depend only on three phases which in turn determine CP violation in
both sectors. The model is comprehensively analysed for its viability and
predictions including the possibility to generate baryon asymmetry through
thermal leptogenesis. It predicts relatively small values for CP phases in the
lepton sector. Successful leptogenesis further restricts the ranges to $-0.4
\le \sin\delta \le 0.4$ for the Dirac phase and $-0.3 \le \sin \eta_1 \le 0.2$,
$-0.5 \le \sin \eta_2 \le 0.5$ for the Majorana phases.
