Can a woman get pregnant by touching a door handle with semen on it and then touch her vagina after?

The sperm in semen become inactive/die soon after they are place in such a setting. They are not tolerant to the environment outside the sites of production or the moist inner female genitalia. It is a good practice to consider door knobs a rich site for germs and washing or sanitizing you hands frequently is always a good idea (& kills sperm).

No. Unless it was a big glob and on purpose. For a pregnancy to happen, the spermatozoon have to be placed in the right environment of the vagina and cervix.They can live for 15-30 min outside the body, but they’re very fragile AND need the right scenario to move fast into the vagina and up the tract. Semen smeared on a surface dries fast affecting he motility. If in doubt, have a pregnancy test.