"Theism" is too loose to really argue about it being rational or irrational with providing specific examples. If I just choose a random theism from a list, the odds are high it will be pretty irrational.

Is it theoretically plausible to create a rational theism? Probably, but getting it qualified as...
a) Theistic
b) Rational
c) Religious

... may find you stuck in a war of semantics.