Direct optical frequency Comb Spectroscopy (DCS) is proving to be a fundamental tool in many areas of science and technology thanks to its unique performance in terms of ultra-broadband, high-speed detection and frequency accuracy, allowing for high-fidelity mapping of atomic and molecular energy structure. Here we present a novel DCS approach based on a scanning Fabry-Perot micro-cavity resonator (SMART) providing a simple, compact and accurate method to resolve the mode structure of an optical frequency comb. The SMART approach, while drastically reducing system complexity, allows for a straightforward absolute calibration of the optical-frequency axis with an ultimate resolution limited by the micro-resonator resonance linewidth and can be used in any spectral region from XUV to THz. An application to high-precision spectroscopy of acetylene at 1.54 um is presented, demonstrating frequency resolution as low as 20 MHz with a single-scan optical bandwidth up to 1 THz in 20-ms measurement time and a noise-equivalent-absorption level per comb mode of 2.7 10^-9 cm^-1 Hz^(-1/2). Using higher finesse micro-resonators along with an enhancement cavity, this technique has the potential to improve by more than one order of magnitude the noise equivalent absorption in a multiterahertz spectral interval with unchanged frequency resolution.