We establish \(C^{\sigma +\alpha }\) interior estimates for concave nonlocal fully nonlinear equations of order \(\sigma \in (0,2)\) with rough kernels. Namely, we prove that if \(u\in C^{\alpha }(\mathbb {R}^n)\) solves in \(B_1\) a concave translation invariant equation with kernels in \(\mathcal L_0(\sigma )\), then u belongs to \(C^{\sigma +\alpha }(\overline{B_{1/2}})\), with an estimate. More generally, our results allow the equation to depend on x in a \(C^\alpha \) fashion. Our method of proof combines a Liouville theorem and a blow-up (compactness) procedure. Due to its flexibility, the same method can be useful in different regularity proofs for nonlocal equations.