In the US, government-run orphanages no longer exist. They were replaced by Foster Care programs in the 1950s.
However, there are private orphanages in the US. This one is dedicated to children who were orphaned due to violence. http://www.theorphansociety.org
The US Foster Care system is well-covered in Wikipedia.
I encourage you to read all three links to become more aware of children who do not have parents to take care of them or children who have been removed from their parents because their parents were harming them.
Here’s a bit of history related to Foster Care:
In the United States, foster care started as a result of the efforts of Charles Loring Brace. “In the mid 19th Century, some 30,000 homeless or neglected children lived in the New York City streets and slums.” Brace took these children off the streets and placed them with families in most states in the country. Brace believed the children would do best with a Christian farm family. He did this to save them from “a lifetime of suffering” He sent these children to families by train, which gave the name The Orphan Train Movement. “[This] lasted from 1853 to the early 1890s [1929?] and transported more than 120,000 [250,000?] children to new lives.” When Brace died in 1890, his sons took over his work of the Children’s Aid Society until they retired. The Children’s Aid Society created “a foster care approach that became the basis for the federal Adoption and Safe Families Act of 1997″ called Concurrent Planning. This greatly impacted the foster care system. Children’s Aid works with the biological and foster parents to “achieve permanency”. “From the mid-1800s to the eve of the Great Depression, orphan train children were placed with families who pre-selected them with an order form, specifying age, gender, hair and eye color. In other cases, trainloads of children were assembled on stages, train platforms or town halls and examined by prospective parents. “Conjuring the image of picking the best apple from the bin. Sometimes a child would be separated from his or her brothers and sisters, or would end up in a family that only wanted them to work. Most of the time the children were chosen by a loving or childless family”.[12
And here are a few statistics:
In 2016, there were 437,465 children in foster care in the United States. 48% were in nonrelative foster homes, 26% were in relative foster homes, 9% in institutions, 6% in group homes, 5% on trial home visits (where the child returns home while under state supervision), 4% in preadoptive homes, 2% had run away, and 1% in supervised independent living. Of 254,114 who exited foster care in 2010, 51% were reunited with parents or caretakers, 21% were adopted, 11% were emancipated (as minors or by aging out), 8% went to live with another relative, 6% went to live with a guardian, and 3% had other outcomes. Of these children, the median length of time spent in foster care was 13.5 months. 13% were in care for less than 1 month, 33% for 1 to 11 months, 24% for 12 to 23 months, 12% for 24 to 35 months, 10% for 3 to 4 years, and 7% for 5 years or more.