As Matt L. said, this is pretty clearly E minor (natural minor, i.e. Aeolian mode). The A chord can be understood as a borrowed chord from the nearby Dorian mode:
X:1
L:1/4
M:
K:C
V:2 clef=treble name="Aeolian"
e, ^f, g, a, b, c d e "C"[e"C (VI)"[e, g, c]
V:1 clef=treble name="Dorian"
e, ^f, g, a, b, ^c d e "A"[a"A (IV)"[a, ^c e]
%
This major IV degree in a minor mode is an extremely common borrowed chord. A great example is Stairway To Heaven, where it is used both to convey a sort of folky mood (Dorian and Mixolydian scales tend to sound a bit celtic on guitar IMO), and to weave in chromatically descending lines.
X:1
L:1/8
M:2/4
K:Am
V:1 clef=treble-8
"III"[g,c']ecc' | "IV"[^f,^f]da,^f | "VI"[f,e]ca,c
%