Polynomials with integer coefficients such that $p(a)=b,p(b)=c,p(c)=a$

While studying polynomials a question struck in my mind that

To have a polynomial $p(x)$ with integer coefficients and $a,b,c$ are three distinct integers, then is it possible to have $$p(a)=b$$ $$p(b)=c$$ $$p(c)=a$$