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We present for the first time a detailed spectroscopic study of chemical element abundances of metal-poor RR Lyrae stars in the Large and Small Magellanic Cloud (LMC and SMC). Using the MagE echelle spectrograph at the 6.5 m Magellan telescopes, we obtain medium resolution (R ∼ 2000−6000) spectra of six RR Lyrae stars in the LMC and three RR Lyrae stars in the SMC. These stars were chosen because their previously determined photometric metallicities were among the lowest metallicities found for stars belonging to the old populations in the Magellanic Clouds. We find the spectroscopic metallicities of these stars to be as low as [Fe/H]spec = −2.7 dex, the lowest metallicity yet measured for any star in the Magellanic Clouds. We confirm that for metal-poor stars, the photometric metallicities from the Fourier decomposition of the lightcurves are systematically too high compared to their spectroscopic counterparts. However, for even more metal-poor stars below [Fe/H]phot < −2.8 dex this trend is reversed and the spectroscopic metallicities are systematically higher than the photometric estimates. We are able to determine abundance ratios for ten chemical elements (Fe, Na, Mg, Al, Ca, Sc, Ti, Cr, Sr and Ba), which extend the abundance measurements of chemical elements for RR Lyrae stars in the Clouds beyond [Fe/H] for the first time. For the overall [α/Fe] ratio, we obtai