An aircraft turbine engine having a compressor,an annular combustion chamber, a system for diffusing and straightening an air stream exiting the compressor in order to supply the combustion chamber, and a heat exchanger, this heat exchanger having: a first circuit supplied with exhaust gas from the turbine engine, and a second circuit comprising an inlet (38ba) connected by a first scroll to an outlet of the diffuser, and an outlet connected by a second scroll to an inlet of the straightener, the scrolls including connecting arms that rigidly connect the annular portions of the scrolls which are secured or connected to the diffuser and to the straightener, respectively.