Mitochondrial aminoacyl-tRNA synthetase that activate and transfer the amino acids to their corresponding tRNAs during the translation of mitochondrial genes and protein synthesis. ATP + L-tryptophan + tRNA(Trp) = AMP + diphosphate + H(+) + L-tryptophanyl-tRNA(Trp) Belongs to the class-I aminoacyl-tRNA synthetase family.