The existing answers make some good points, particularly: (1) the physical/biological demands of crucifixion; and (2) that Jesus announces his thirst. He does not, in fact, "ask for a drink" (OP's original concern), and this is vital for understanding the gospel at this point.
Because there is also a textual response. In manner distinct from the synoptic gospels, John portrays Jesus as very much in control throughout his crucifixion, despite appearances. The principle is spelled out in John 10:17-18:
17 The reason my Father loves me is that I lay down my life—only to take it up again. 18 No one takes it from me, but I lay it down of my own accord. I have authority to lay it down and authority to take it up again. This command I received from my Father.
Then at three points during the crucifixion scene, the "fulfillment of "scripture" is invoked, underscoring this notion:
- v. 24, casting lots for the "robe" (cf. Ps 22:18);
- v. 28, Jesus' drawing on Ps 69:21 in announcing his thirst; and
- v. 36-37, the spear-thrust in preference to leg-breaking (cf. Ps 34:20; Zech 12:10).
Five times in John's gospel a formula of scripture fulfillment is used. Four of those use plēroō = "fulfill". Only in 19:28 -- the "I thirst" verse -- does it use teleioō = "complete", no doubt to reinforce Jesus' final word from the cross (v. 30, "It is finished" = tetelestai). (In fact, of the 11 occurrences in the NT, this is the only one that doesn't use plēroō.)
Quite simply, Jesus announces his thirst in order to fulfill scripture (ἵνα τελειωθῇ ἡ γραφὴ).
While there were good "physical" reasons why Jesus would be thirsty, John reports Jesus as announcing his thirst for clear and overt theological reasons. John's Jesus is fulfilling his mission, and the moment of "thirst" in v. 28 is a deliberate act to that end.