According to Sitecore documentation you can run query stored on an item using
/item/{id}/query
url. You must replace the {id}
part with the item which stores the query, e.g.
/sitecore/api/ssc/item/110D559F-DEA5-42EA-9C1C-8A5DF7E70EF9/query
You can add more parameters, e.g. pageSize, page, database, includeStandardTemplateFields, fields:
/sitecore/api/ssc/item/110D559F-DEA5-42EA-9C1C-8A5DF7E70EF9/query?pageSize=10&page=5
Description for all of the can be found in the link above.
There is a Query Definition
template which you should use to store your query. Just create an item using that template. You can find it in Sitecore with /sitecore/templates/System/Services/Item Service/Query/Query Definition
path: