Change $C^1$-embedding to a homotopic $C^\infty$-embedding

Question

I have a $C^1$-embedding of $\mathbb{S}^1$ into some smooth manifold. How do i prove, that there exists a homotopic $C^\infty$-embedding of $\mathbb{S}^1$? Is it easier for some $r\geq 3$ to prove, that a homotopic $C^r$-embedding embedding exists? And if so how?