The U.S. government does not expressly forbid spouses seeking a green card and living abroad from visiting their sponsoring spouses in the United States while their marriage green card application is pending. But doing so is generally discouraged because of the risks involved.
Technically, the spouse seeking a green card can visit their sponsoring spouse by applying for a visitor visa, such as a tourist visa, that is intended for a short, temporary stay in the United States. The spouse seeking a green card could then travel to the United States but would need to return to their home country before the tourist visa expires.
Unfortunately, it's often not that simple. The chances of being approved by the U.S. government for a tourist visa are much lower when a marriage green card application has been filed. This is because the "intents" of the two visas — the reasons for coming to the United States — would conflict: Again, a tourist visa is intended only for a short-term visit, whereas a marriage-based green card (or "spousal visa") is intended for permanent residence in the United States.
Over the years, many spouses seeking a green card have purposely stayed past the expiration date of their tourist visa to continue the marriage green card process from within the United States. The U.S. government considers this practice a "willful misrepresentation" of one's intentions — in other words, a lie — and therefore flags those who enter the United States for conflicting reasons.
If an immigration officer at a port of entry (POE), such as a U.S. airport, becomes aware that a traveler is married to a U.S. citizen or green card holder and has a pending marriage green card application, the traveler (spouse seeking a green card) is often forced to return to their home country, usually as soon as arriving. The consequences are greater when the traveler has lied about their intentions for entering the United States.
As you can see, this situation can be complicated, so we've put together a more detailed guide to the issues involved in visiting a spouse in the United States.