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In this paper, we study twisted arithmetic divisors on the modular curveX_0(N) with N square-free. For each pair (\Delta, r) where \Delta >0 and \Delta\equiv r^2 \mod 4N, we constructed a twisted arithmetic theta function\phi_{\Delta, r}(\tau) which is a generating function of arithmetic twistedHeegner divisors. We prove the modularity of \phi_{\Delta, r}(\tau), along theway, we also identify the arithmetic pairing \langle \phi_{\Delta,r}(\tau),\widehat{\omega}_N \rangle with special value of some Eisensteinseries, where \widehat{\omega}_N is a normalized metric Hodge line bundle.

Twisted arithmetic Siegel Weil formula on X0(N)