it is noted that the key signature is D major
If you mean the song by Simon and Garfunkel the signature of D major would be 2 sharps (F#,C#) and it must be in E-dorian, and the C# would be the major 6th of dorian. That means we have a major IV (A) like Richard says.
Most images (sheet music) I found are in minor (looking like aeolian) with an additional accidental (major 6th!) what indicates that this must be dorian.
You'll find searching by images two different versions in d, one has the signature of of C-major => d dorian, another 1 flat=> d-minor (aeolian)
The following version (s. image) must be identical with yours (additional accidental=C#)
This one is notated in E-aeolian - compared with yours - it has only 1 sharp in signature and an additional sharp (C#) as an accidental. So don't mind so much the mode as the final chord will be the tonic (and here obvious the 1st note too!)
So Em = i, D=VII, A=IV, G=III
The problem has been discussed already here in Dorian of G (G-dorian) but we miss the signature of 1 sharp so it looks like aeolian of C (a-aeolian) with additional F#:
Analysis of Scarborough Fair
Read what Scott Wallace has written in his answer:
A short answer: Scarborough Fair is not in the minor, but is modal: Dorian (that's where the major IV chord comes from) and Aeolian (the minor iv). The modal character is underscored by the progression VII-i, which is normal for Dorian and Aeolian, and the fact that there is no major V chord.