Given a crane's long neck and how the bird hunts, possibly related to 蔓 (tsuru, “vine”); 弦 (tsuru, “bowstring; musical instrument string”); 釣る, 吊る (tsuru, “to hang down; to string up; to fish”).
Given how cranes flock together, possibly related also to 連る (tsuru), older root form of modern verb 連れる (tsureru, “to accompany”). That said, 連る also appears to ultimately derive from 蔓 (tsuru, “vine”).
Likely Altaic cognates include Proto-Turkic *durunja (“crane”) (whence Turkish turna), Korean 두루미 (durumi, “crane”), Mongolian тогоруу (togoruu, “crane”)|tr=togoruu). Compare also Hungarian daru (“crane”).
The reading tsuru is first seen used to mean a crane (the bird) from the late Heian period.
Prior to that time, the only reading used for the bird was tazu. However, the kanji 鶴 was used in the Man'yōshū as a phonetic ateji for the verb ending -tsuru, suggesting that tsuru may have already existed as an everyday term meaning a crane.[1]
[1] ↑ Jump up to: 1.0 1.1 1.2 1988, 国語大辞典（新装版） (Kokugo Dai Jiten, Revised Edition) (in Japanese), Tōkyō: Shogakukan