Can a US citizen who resides outside the US apply for a green card for their spouse?

Yes that is possible and the US citizen can sponsor his spouse at the US consulate overseas, but a requirement To sponsor his spouse is that The sponsor has a US domicile, meaning that the permanent residence of the sponsoring spouse is in the United States, sometimes the government will allow the married couple to avoid that requirement if they can prove that they have taken significant steps to relocating back to the United States like for example hiring a moving company signing a lease buying property obtaining the US drivers license, etc. But I always advise people in that situation to have the US citizen spouse relocate back to the United States in advance of the foreign national getting the green card and coming over here.Furthermore, a case such as this should not be done by yourself, it really should be done with the aid and representation by an immigration attorney.