Not a generic sort field, but say a list of document IDs I want returned in that order.
Example: document_ids = [5, 3, 10, 6]
Can I query solr for documents 5, 3, 10, 6 in that order?
You can use the bq param (Boost Query) for this and then sort by score, which is default.
q=id:5+OR+id:3+OR+id:10+OR+id:6&bq=id:5^4+id:3^3+id:10^2
As you can see within the bq parameter each of the IDs gets a declining boost value, until the last one - in your case 6 - does not receive any boost any more. Since you search by ID, each document would have the same score, so boosting them that way will get you the sort order you want.
Some reference about the parameter
In case you are using the Standard Request Handler or the (e)DisMax this works in any case
q=id:5^4+OR+id:3^3+OR+id:10^2+OR+id:6
This makes use of Term Boosting, which is explained in the reference documentation below the topic Boosting a Term with ^. The logic keeps the same as above.