The answer is yes. Yes you can. In the U.S., at least.
Further, nearly every person in the U.S. has been exposed to HPV and/or is carrying it. (well, that's an exaggeration. I looked it up and the actual number is estimated at 79 million people currently carrying it, and 80% of all sexually active men and women. I calculate the incidence rate as being over 24,000/100,000 people. In other words, it's essentially unavoidable. And you don't even have to have actual sex to catch it.
Working from memory here: HPV is a group of about 20 different types of viruses. It's the virus that causes garden variety warts, and cold sores, and essentially benign infections like that. A couple of the viruses can possibly lead to infections that can possibly lead to cervical cancer. This is why women get regular Pap tests. In nearly all cases (in the U.S.) the pre-cancerous cells are detected by the Pap test and the cells can be removed. It is regarded as the only cancer that is 100% curable.
In developing nations, cervical cancer is one of the leading causes of death among women. Evita Peron died from it.