The Collaborative International Dictionary of English v.0.48:

Woo \Woo\, v. t. [imp. & p. p. Wooed; p. pr. & vb. n.
   Wooing.] [OE. wowen, wo?en, AS. w?gian, fr. w?h bent,
   crooked, bad; akin to OS. w[=a]h evil, Goth. unwahs
   blameless, Skr. va?c to waver, and perhaps to E. vaccilate.]
   [1913 Webster]
   1. To solicit in love; to court.
      [1913 Webster]

            Each, like the Grecian artist, wooes
            The image he himself has wrought.     --Prior.
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   2. To court solicitously; to invite with importunity.
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            Thee, chantress, oft the woods among
            I woo, to hear thy even song.         --Milton.
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            I woo the wind
            That still delays his coming.         --Bryant.
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The Collaborative International Dictionary of English v.0.48:

Woo \Woo\, v. i.
   To court; to make love. --Dryden.
   [1913 Webster]

WordNet (r) 3.0 (2006):

woo
    v 1: seek someone's favor; "China is wooing Russia" [syn: woo,
         court]
    2: make amorous advances towards; "John is courting Mary" [syn:
       woo, court, romance, solicit]

Moby Thesaurus II by Grady Ward, 1.0:

50 Moby Thesaurus words for "woo":
   address, allure, angle for, bait, bait the hook, beau, bid for,
   bill and coo, blandish, cajole, canvass, chase, coax, court, decoy,
   draw, draw in, draw on, ensnare, entice, esquire, fish for, flirt,
   flirt with, follow, give the come-on, inveigle, lay siege to,
   lead on, look for, lure, make suit to, make up to, offer bait to,
   pay attention to, pay court to, pop the question, pursue, rope in,
   seduce, seek, serenade, solicit, spark, squire, suck in, sue,
   sue for, swain, sweetheart