I am a US citizen living abroad, can I sponsor my wife for her Green Card?

You essentially have to go through the same process that you would in the United States.
Some embassies will allow you to go through the process there if you have resided in that country for a certain period of time.
Some countries have immigration offices to assist with the process, for example it is not uncommon in London, Rome, and India to do so.

What is a “U Visa” in the United States?
When an illegal immigrant is a victim of a serious crime within the country, they are usually afraid to go to law enforcement to assist them in solving the crime. In the event of this, the United States offers a type of visa for victims of a crime that wish…
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Adjustment of Status in The United States
When a foreign individual wishes to come to the United States, they must be approved for a certain status. This is typically done through different types of visas. These statuses allow an individual to come to the country for several reasons. This can include visitation, employment, school, marriage, and more.…
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Fiance Visas in the United States
Individuals who are citizens of the United States and engaged to a non-citizen may be able to bring their fiance to the country. This requires them to apply for a visa for their entry to the country so that they may be married and live within the United States. This…
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Deportation Laws in the United States
Foreign individuals living in the United States need to maintain a certain status in order to live in the country. Those individuals must follow a certain set of immigration laws that allow them to remain within the country. Their status within the country may be affected if they violate…
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