Books online link: http://technet.microsoft.com/en-us/library/bb934196.aspx
Page title: CREATE SPATIAL INDEX (Transact-SQL)
Under sub-header "Permissions" states:
"Requires ALTER permission on the table or view. User must be a member of the sysadmin fixed server role or the db_ddladmin and db_owner fixed database roles."
The article suggests that a login with "sysadmin" or "db_ddladmin" and "db_owner" roles are allowed to create a spatial index.
However, I find that ALTER permission on the table object alone will allow creating a spatial index on a table.