Scales to Play Over D#7
Every chord is a subset of several scales: any scale that contains all of a chord's tones fits over it. Pick a chord to see the matching scales from its own root, the major keys the chord belongs to, and full fretboard diagrams for every scale on guitar.
A D#7 chord contains the notes D# – G – A# – C#. Any scale that includes every one of those 4 tones fits over it — from the root D#, that means D# Mixolydian, D# Dorian Bebop, D# Mixolydian Bebop, D# Half Whole Diminished, D# Spanish and D# Gypsy Major. Start with the first scale listed: it is the most common choice, and the others color the same chord tones differently.
D#7 is also diatonic to one major key: G# major (relative minor Fm). In a song from one of those keys you can also solo with the key's own major scale or its relative minor pentatonic across the whole progression, not just this chord.