We report a new technique to map the orientational anisotropy of paramagnetic systems without physically changing the crystal orientations in near zero-field (NZF) pulsed EPR experiments. By implementing three sets of orthogonal coils around the sample, we are ble to create a magnetic vector up to 2 mT in any three-dimensional orientation in space. In NZF region, the hyperfine tensor elements are comparable to the electronic Zeeman interaction energy, thus very rich spectral patterns can be obtained by "dialing" in a magnetic field vector without moving the sample. The technique further allows us to examine the site symmetry of organic crystals and powdered solids doped with chromophores which can be photo-excited to the triplet state by laser light. The technique is exemplified in the study of pentacene in p-terphenyl crystals.