Yes, you can. Order is just a relation, i.e. a set that contains pairs of elements. So for example, let X be the relation <. X is a subset of NxN, the cartesian product of N. We say that n<m if the pair (n,m) is in X. Moreover, we say that (n,n+1) is in X, and whenever (n,m) in X and (m,k) in X, then (n,k) in X. This constitues order on naturals.