A US citizen who is at least 21 can petition their parent(s) to immigrate to the US. Whether the parent can actually get an immigrant visa may depend on whether they are subject to any bans and other factors. Having left the US on voluntary departure does not imply that they have or do not have a ban, it just means they were put into deportation proceedings in the US.The most likely potential ban is if the parent accrued at least 1 year of u201cunlawful presenceu201d in the US before leaving, they would have a 10 year ban from the day of leaving (whether someone accrued u201cunlawful presenceu201d is complicated and cannot be determined without more information). If they have this ban and wish to immigrate before the ban is up, then they will need to apply for a waiver, which will need to demonstrate u201cextreme hardshipu201d to their parent who is a US citizen or permanent resident if they cannot be in the US.Depending on the exact circumstances, they may have additional bans, for example, if they previously accrued 1 year of u201cunlawful presenceu201d and subsequently entered the US again illegally, or was previously deported and subsequently entered the US again illegally, then they have a lifetime ban, which there is no way to overcome until they have spent 10 years outside the US. Again, more details will be needed to determine what bans, if any, they may have.