Yes, your family can visit on a tourist visa (like a B-2 visa in the U.S.).But they are only allowed to stay temporarily, usually for 6 months or less.

A tourist visa is meant for visiting, not living, working, or studying long-term and if they overstay, it can lead to serious problems, like visa bans or deportation.

Applying for permanent status while on a tourist visa might look like they misused the visa, especially if planned before entering because the Border agents can deny entry if they believe someone plans to stay long-term on a tourist visa so It’s always best to use the correct visa for the purpose — if they want to live with you, family sponsorship is the safer path