If you are filing an I-130 for your parent, they can generally travel to the U.S. on a visitor visa while the petition is pending. Theoretically, they could face issues at entry due to the pending green card application, but in practice, parents of U.S. citizens are rarely stopped for this reason.
To reduce the risk of being denied entry, consider having your parent use an immigration pre-clearance airport, like Abu Dhabi or Dublin, so they can return home easily if denied. While past practices suggest minimal issues, policies could change, especially under unpredictable administrations.