This song is more commonly known as "Katibim". Turkish lyrics (with diacritical marks) are HERE (Scroll down to the end of the page). And HERE. MIDI can be obtained much more easily with this title "Katibim"; HERE, HERE (Click on "FOLK"), and other sites. Audio recording by Safiye Ayla is HERE (the title is "Kbtibim" here, though). It's on Various Artists, Masters of Turkish Music, V. 2 (Rounder CD 1111). For info on Eartha Kitt and this song, see this page (in Turkish; I wish I could read it).
Printed version (with tune, chords, English words) of "Üsküdar" is in Charles Haywood, ed., Folk Songs of the World (John Day Company, 1966, p. 209):

1. [Em]As I walked [Am]one rainy [Em]morn'
The [Am]road to Üskü[Em]dar,
[Em]As I walked [Am]one rainy [Em]morn'
The [Am]road to Üskü[Em]dar,
[C]There I saw my [Em]dear beloved,
[Am]Coimg from a[B7]far.
[C]There I saw my [Em]dear beloved,
[Am]Coming [B7]from a[Em]far.

2. On the road I later found
A kerchief of finest cloth, (2 lines; x2)
Cleaning it with tend'rest care,
Surely 'twas his, I thought. (2 lines; x2)

3. Anxiously I looked for him,
When he appeared near me;
Promising to wander no more,
Mine he'll forever be.

(English version by Charles Haywood)

~Masato