Currently standardized Direct Anonymous Attestation (DAA) schemes have their security based on the factoring and the discrete logarithm problems, and are therefore insecure against quantum attackers. This paper presents a quantum-safe lattice-based Direct Anonymous Attestation protocol that can be suitable for inclusion in a future quantum-resistant TPM. The security of our proposed scheme is proved in the Universal Composability (UC) model under the assumed hardness of the Ring-SIS, Ring-LWE, and NTRU problems. The signature size of our proposed DAA scheme is around 2MB, which is (at least) two orders of magnitude smaller compared to existing post-quantum DAA schemes.