Suppose we have the inhomogeneous advection equation $$\left(\frac{\partial}{\partial x}+\frac{1}{c}\frac{\partial}{\partial t}\right)u(t,x)=v(t,x)$$ for $u,v:\mathbb{R}\times\mathbb{R}\to\mathbb{R}$ (with boundary conditions not yet specified).
Assuming that we had no $v$, i.e. the homogeneous part of the equation, the Crank-Nicolson method would yield
$$-c\frac{\mu}{4}u^{n+1}_{\ell-1}+u^{n+1}_{\ell}+c\frac{\mu}{4}u^{n+1}_{\ell+1}=c\frac{\mu}{4}u^n_{\ell-1}+u^n_{\ell}-c\frac{\mu}{4}u^n_{\ell+1},$$
where $\mu=\frac{\Delta t}{\Delta x}$ and $u^n_\ell=u(n\Delta t,\ell\Delta x)$.
I don't know how to deal with the inhomogeneity in these schemes though.