Your question is based on a misunderstanding, which is "there must be a single scale fitting a chord progression". This is usually wrong; many interesting chord progressions are not based on the notes of a single scale. The chords in your progression have a C (C major) and a C# (A major), which, as you've noted, usually don't occur in the same scale.
There are two ways to get around this when playing a melody / improvising over such a progression. Either you skip the "dangerous" notes; i.e., you avoid both the C and the C#. This will leave you with an E minor pentatonic scale, maybe with an added F# (i.e., an E natural minor scale without the sixth note). The other option is to use both the C and the C#, but only where they fit the chords, i.e., use a C over C major, and a C# over A major.
Most people will hear this progression in the key of E minor. Note that the key of E minor is not a single scale, but the union of E natural minor, E harmonic minor, and E melodic minor. And in this way the C as well as the C# become available; the same is true for the D and the D#; the latter doesn't occur in your progression, but it could; try:
|| Em | A | C | D B7 ||
To most ears this would sound as a perfectly conventional progression, and its chords contain a C, a C#, a D, and a D#.
For more information on minor key harmony have a look at this postthis post.
