The twist-deformed conformal algebra is constructed as a Hopf algebra with twisted co-product. This allows for the definition of conformal symmetry in a non-commutative background geometry. The twisted co-product is reviewed for the Poincar�� algebra and the construction is then extended to the full conformal algebra. It is demonstrated that conformal invariance need not be viewed as incompatible with non-commutative geometry; the non-commutativity of the coordinates appears as a consequence of the twisting, as has been shown in the literature in the case of the twisted Poincar�� algebra.

8 pages; REVTeX; V2: Reference added