Can "candidate" be used as a verb?

Yes, the noun candidate can be used as a verb. Verbing nouns is very common in English. However, in a very formal setting such as a job application, I would avoid it. Instead, I'd suggest the following solution:

"I am applying for the position of blah, blah, blah"

1. The important thing is to understand that the interviewer must understand the candidate's personality and if he/she is fit for the position where he is candidated. source
2. Maybe he's candidating for the UCA ministry? source
3. Like a number of human politicians, such as the Queensland Premier, Loupi lives outside the electorate he's candidating for. If you want to know more about him, ... source
4. I think she should be on the ballot and I would vote for her no matter what she was candidating for. She is brilliant, has a kindness about her ... source
5. The contest is open to all artists regardless of age, sex, nationality or artistic curriculum and can participate with no more than 3 works; they can be candidated even in different sections. source

The OED lists this as

candidate, v. 2

U.S. colloquial.
To stand as a candidate.

• 1848 J. R. Lowell Biglow Papers 1st ser. viii. 122 The can'idatin' line, you know, 'ould suit me to a T... So I'll set up ez can'idate fer any kin' o' office.
• 1884 Cent. Mag. June 308/1 Let him put the question to some [choir-singers] who every spring have to candidate for a situation.
• 1909 Springfield (Mass.) Weekly Republican 2 Sept. 14 Mr. Seccombe candidated in the Goschen church last spring.

Not being in the U.S. myself, I'd look at you oddly if you said you were "canditating for this position".

While there is a tradition of "verbification", it's not advised to coin a new verb yourself in formal speech, especially if an appropriate verb -- in your case applying -- is available. Unmoderated verbing weirds language.

Candidate (Dictionary.com)

verb (used without object) can·di·dat·ed, can·di·dat·ing.

to become a candidate for service as a new minister of a church; preach  before a congregation that is seeking  a new minister.

As a BE speaker, novel verbing of a noun makes the speaker sound like they are speaking AmE. If it's common to create new terms, it's in American English rather than British English. I guess what I am saying is it's probably more acceptable to citizens of the US than to those of the UK. In the UK many of them grate and most such usages should be avoided. There are some examples in BE (for instance abusing the name of a maker of vaccum cleaners, most BE speakers would not find 'hoovering' at all out of place, whereas the verbing of 'medal' as in 'Usaine Bolt is medalling' is something only a few sports commentators use in BE) but fewer than AmE.