Viruses don't make their own proteins because they are not cells. A virus is a nucleic acid enclosed in a protein coat, and does not contain organelles. Bacteriophages, viruses that target bacteria as a host, inject their genetic material into the host bacterial cell. Therefore, cells don't even need proteins, (not including their protein coat) so they do not make them.
*Keep in mind that since there are no organelles, there are no ribosomes for the RNA (ribonucleic-acid) to deliver the coded message and amino acids to.