Only you need an order line field in your table.
In RadzenGrid you can add a field for reordering and two buttons. One button will call the UP function and the other one will call the DOWN function.
Add a new column without field and create a template
Add your buttons
Add your events
The UP function will change the active record's orderLine field to (n -1) and the previous record orderLine field to (m+1). You need to an exception for the first record (This record can't move up).
The DOWN function will work vice versa. The exception must work for the last record.
And your RadzenGrid's data source needs an ordering parameter for the orderLine field.