The electronic properties of armchair graphene nanoribbons (AGNRs) can be significantly modified from semiconducting to metallic states by applying a uniform perpendicular magnetic field (B-field). Here, we theoretically study the band gap modulation induced by a perpendicular B-field. The applied B-field causes the lowest conduction subband and the topmost valence subband to move closer to one another to form the n=0 Landau level. We exploit this effect to realize a device relevant magnetoresistive (MR) modulation. Unlike in conventional spin-valves, this intrinsic MR effect is realized without the use of any ferromagnetic leads. The AGNRs with number of dimers, Na=3p+1[p=1,2,3,…] show the most promising behavior for MR applications with large conductance modulation, and hence, high MR ratio at the optimal source-drain bias. However, the MR is suppressed at higher temperature due to the spread of the Fermi function distribution. We also investigate the importance of the source-drain bias in optimizing the MR. Lastly, we show that edge roughness of AGNRs has the unexpected effect of improving the magnetic sensitivity of the device and thus increasing the MR ratio.