Yes (see here for details)

Arguments:

(required) long : folderid -  the id of the album
(required) long : newposition - the new position of the album within the category 
(required) string : publickey - publickey of an application
(required) string : token - the access token

Request Example:

http://www.bluemelon.com/api/rest/{api_sign}/
?method=bluemelon.albums.changeposition&folderid=5&newposition=10&publickey={publickey}&token={token}

Response Example:

<rsp status="ok" onrequest="bluemelon.albums.changeposition" />

Error Codes:

4 - "Missing parameter"
5 - "Invalid parameter"
12 - "Application not found"
14 - "Invalid accessToken"
16 - "Access token timed out.You must relogin."
17 - "Invalid call signature size"
18 - "Invalid call signature"
20 - "Missing api_sign"
600 - "No write permissions"
601 - "Mismatched parameter in your request"
602 - "No read permissions"
603 - "Account recently expired or deleted"