Data, like his "brother" Lore, was created by engineer, scientist, and inventor Dr. Noonien Soong on the planet Omicron Theta, which was stripped by the so-called Crystalline Entity — see "Datalore".
If you watch this episode and other episodes of TNG dealing with Data's back story, you will see that the colony on Omicron Theta was not especially technically advanced. Given that Soong's primary goal was to create a fully functional positronic neural net (Data's brain) inside a humanoid shell, and given the general lack of technology elsewhere in the colony, I would say that it was not high on Dr. Soong's priority list to give him the ability to access computers and other electronic devices by non-humanoid means.
One could ask, why wouldn't Starfleet or Geordi later augment Data to have that ability, given how useful it might be? It was emphasized many times in TNG that most members of the Enterprise D crew consider Data to be an autonomous life form, and so they likely would frown upon such suggestions as disrespectful. (Earning this respect was not always easy: Dr. Pulaski, case in point.)
But actually, Data's brain has been directly "plugged" into the Enterprise computer and other computer systems many times in TNG. So it is not true actually that Data always has to "use" a computer manually in Star Trek. (See the nice screenshot in Einer's answer above.)
Furthermore, by interfacing with Locutus in "The Best of Both Worlds (part 2)", Data was able to input commands directly into the neural net of a Borg cube, forcing all of the Borg on board to enter their regeneration cycle. This demonstrates at least two types of interface at once: direct physical connection from Data's positronic brain to other devices (Locutus' Borg implants) and Data's connection, in turn, to the Borg Collective (a "wireless" connection, if you like, over subspace).
Also see: "A Fistful of Datas".
I also wish to explicitly counter the comment by "The Spooniest" made below the original question. Data was not "designed to function as a crew member". He was found by chance on Omicron Theta by Starfleet officers, and his own career in Starfleet came later.