Ral Zareks first Ability: Magic The Gathering
Yes, you can. You must choose a 'target permanent' for the first part of the ability; the ability doesn't specify you must choose an untapped permanent. The ability won't be able to tap that permanent:


  701.20a To tap a permanent, turn it sideways from an upright position. Only untapped permanents can be tapped.


but that's not a problem; to activate an ability you must choose valid targets, it doesn't matter if the ability resolves fully. Part of activating an ability is paying its cost, which in this case is adding a loyalty counter:


  606.4. The cost to activate a loyalty ability of a permanent is to put on or remove from that permanent a certain number of loyalty counters, as shown by the loyalty symbol in the ability’s cost.


During resolution, even if the first part of the ability doesn't do anything, the second part is still carried out:


  608.2c The controller of the spell or ability follows its instructions in the order written.