We initiate the study of algorithms for constraint satisfaction problems with ML oracle advice. We introduce two models of advice and then design approximation algorithms for Max Cut, Max $2$-Lin, and Max $3$-Lin in these models. In particular, we show the following. 1. For Max-Cut and Max $2$-Lin, we design an algorithm that yields near-optimal solutions when the average degree is larger than a threshold degree, which only depends on the amount of advice and is independent of the instance size. We also give an algorithm for nearly satisfiable Max $3$-Lin instances with quantitatively similar guarantees. 2. Further, we provide impossibility results for algorithms in these models. In particular, under standard complexity assumptions, we show that Max $3$-Lin is still $1/2 + η$ hard to approximate given access to advice, when there are no assumptions on the instance degree distribution. Additionally, we also show that Max $4$-Lin is $1/2 + η$ hard to approximate even when the average degree of the instance is linear in the number of variables.