Voice recording is the recording and playback of sound waves. The first device able to record the human voice was the phonoautograph in 1857, so the answer to your question is yes.

"The first practical sound recording and reproduction device was the mechanical phonograph cylinder, invented by Thomas Edison in 1877 and patented in 1878" - from the wikipedia page on sound recording

Your recorded voice will sound strange to your ears. But will not sound strange to someone else comparing your natural voice with a recording.

What singer dubbed her voice onto recording made by her father.

Use a low cost recording equipment.