Context. T Tauri stars are known to be the cradle of planet formation. Most exoplanets discovered to date lie at the very inner part of the circumstellar disk (<1 au). The innermost scale of young stellar objects is therefore a compelling region to be addressed, and long-baseline interferometry is a key technique to unveil their mysteries. Aims. We aim to spatially and spectrally resolve the innermost scale (≤1 au) of the young stellar system CI Tau to constrain the inner disk properties and better understand the magnetospheric accretion phenomenon. Methods. The high sensitivity offered by the combination of the four 8-m class telescopes of the Very Large Telescope Interferometer (VLTI) allied with the high spectral resolution (R ~ 4000) of the K-band beam combiner GRAVITY offers a unique capability to probe the sub-au scale of the CI Tau system, tracing both dust (continuum) and gas (Brγ line) emission regions. We developed a physically motivated geometrical model to fit the interferometric observables – visibilities and closure phases (CP) – and constrained the physical properties of the inner dusty disk. The continuum-corrected pure line visibilities have been used to estimate the size of the Hydrogen I Brγ emitting region. Results. From the K-band continuum study, we report a highly inclined (i ~ 70°) resolved inner dusty disk, with an inner edge located at a distance of 21 ± 2 R★ from the central star, which is significantly larger than the dust sublimation radius (Rsub = 4.3 to 8.6 R★). The inner disk appears misaligned compared to the outer disk observed by ALMA and the non-zero closure phase indicates the presence of an asymmetry that could be reproduced with an azimuthally modulated ring with a brighter south-west side. From the differential visibilities across the Brγ line, we resolved the line-emitting region, and measured a size of 4.8- 1.0+ 0.8 R★. Conclusions. The extended inner disk edge compared to the dust sublimation radius is consistent with the claim of an inner planet, CI Tau b, orbiting close in. The inner-outer disk misalignment may be induced by gravitational torques or magnetic warping. The size of the Brγ emitting region is consistent with the magnetospheric accretion process. Assuming it corresponds to the magnetospheric radius, it is significantly smaller than the co-rotation radius (Rcor= 8.8 ± 1.3 R★), which suggests an unstable accretion regime that is consistent with CI Tau being a burster.