Using Raman spectroscopy, we demonstrate that the anisotropic interaction between single-walled carbon nanotubes (SWNTs) and poly(methyl methacrylate) (PMMA) causes significant changes in the electronic properties of their composites. Two different procedures were used to prepare the composites: melt blending and in-situ UV polymerization. Resonant Raman studies relate the electronic density of states (DOS) of the SWNTs to the corresponding vibration symmetry changes of both the PMMA and the SWNTs. Our results show that, in the melt-blended sample, the SWNTs—originally semiconducting—became predominantly metallic. The changes in the electronic properties were also confirmed by dielectric constant measurements. We propose that the anisotropic interaction between PMMA and SWNTs in the melt-blended composite is the dominant reason for the observed electronic character change.