In this paper, we propose and study a semi-random model for the Correlation Clustering problem on arbitrary graphs G. We give two approximation algorithms for Correlation Clustering instances from this model. The first algorithm finds a solution of value $(1+ \delta)optcost + O_{\delta}(n\log^3 n)$ with high probability, where \optcost is the value of the optimal solution (for every $\delta > 0$). The second algorithm finds the ground truth clustering with an arbitrarily small classification error $\eta$ (under some additional assumptions on the instance).