  The recent characterization of transiting close-in planets has revealed an
intriguing population of sub-Neptunes with highly tilted and even polar orbits
relative to their host star's equator. Any viable theory for the origin of
these close-in, polar planets must explain (1) the observed stellar
obliquities, (2) the substantial eccentricities, and (3) the existence of
Jovian companions with large mutual inclinations. In this work, we propose a
theoretical model that satisfies these requirements without invoking tidal
dissipation or large primordial inclinations. Instead, tilting is facilitated
by the protoplanetary disk dispersal during the late stage of planet formation,
initiating a process of resonance sweeping and parametric instability. This
mechanism consists of two steps. First, a nodal secular resonance excites the
inclination to large values; then, once the inclination reaches a critical
value, a linear eccentric instability is triggered, which detunes the resonance
and ends inclination growth. The critical inclination is pushed to high values
by general relativistic precession, making polar orbits an inherently
post-Newtonian outcome. Our model predicts that polar, close-in sub-Neptunes
coexist with cold Jupiters in low stellar obliquity orbits.
