  Iridium oxides have provided a playground to study novel phases originating
from spin-orbit coupling and electron-electron interactions. Among them, the
d-wave singlet superconductor was proposed for electron-doped Sr$_2$IrO$_4$,
containing two Ir atoms in a unit cell due to the staggered rotation of oxygen
octahedra about the c-axis. It was also noted that such oxygen octahedra
rotation affects electronic transports. Here we study the role of octahedra
tilting away from the c-axis, in determining superconducting pairing symmetry.
We show that the octahedra tilting changes the large Fermi surface to a Dirac
point, which strongly suppresses the conventional d-wave pairing. Furthermore,
it also promotes effective spin-triplet interactions in the strong Hubbard
interaction limit, leading to a transition from the even-parity to odd-parity
superconducting phase. Thus, tuning octahedra distortions can be used as a tool
to engineer a spin triplet superconductor in strongly correlated systems with
strong spin-orbit coupling.
