In this work, the authors adapt to the case of a global field \(F\) of positive characteristic, that is, a field of functions over a finite field \(\mathbb{F_q}\), the results proved for a number field in Labesse-Waldspurger's book La formule des traces tordue d'après le Friday Morning Seminar. In other words, the authors establish the trace formula for a twisted \(G\)-space \(\widetilde G\), where \(G\) is a connected reductive group defined over \(F\). This is a first step towards the stabilized form of the twisted trace formula, necessary for most applications, which is the subject of ongoing work.