How to avoid the repetition of "I" while writing a cover letter for an academic job?

Because it's a cover letter, I think it's quite natural that you say a lot about you in it. That's actually not to be avoided, because you want to give the addressee a good idea of your background, your motivations, your interests, etc. In short, you want to show them who you are, so they want to work with you. This is a totally different exercise than usual academic writing.

Now, regarding the redundancy of I, it is a matter of writing style. It probably wouldn't bother me much, but if you want to diminish it for some reasons, here are worthy alternatives:

• Instead of starting your sentence with I, just push it somewhere down in some sentences. That way, you avoid the pattern of I as the first word of every sentence.

  Looking at your group's wide range of research, I must confess a certain attraction for your recent groundbreaking work on the correlation between beer-drinking and publication rate.

 

• Use constructions that, while retaining the first person, shift from the subject pronoun to other cases:

  It has been my intention for a few years now to shift my research interests from pure psychology to experimental psychohistory, and I have thus taken in 2009 a post-doc position at the University of Trentor (group of prof. Seldon)

  instead of “I decided a few years ago to move to the field of psychohistory…”. Similarly, you could say

 

• The standard techniques of academic writing… introduce the pronoun once, then shift the discuss to avoid being the actor, e.g. using passive voice.

  During my thesis, I introduced a new data reduction technique called XXZ. This algorithm, when applied to large datasets, was used to univocally establish whether data was being manipulated. In particular, results obtained on the 2000 election showed systematic bias against a specific candidate, highlighting its power as a diagnostic tool for real-life applications.

 

Be aware that there are downsides, though: most of these alternatives are longer than a direct sentence starting with I, which means overusing them could make you sound windy.

One possibility is to use "my" now and then: instead of "I am experienced in ...", write "My fields of experience include ...". Another possibility is to use references to previous sentences: instead of writing "I developed the method of ... . I applied it to the problem of ... ." write "I developed ... . Its application to ... resulted in ... .". Also, instead of writing "I'm interested in the position because ...", write "This position will allow me to ... and benefit my ...". The idea is always the same: look at all other words in the sentence and think of whether one of them can be made the subject without changing the meaning or diluting the "importance" of the sentence. If it can, do it. If not, resort to passive voice and other techniques suggested in this thread. If it is still not satisfactory for some reason, just use "I" and go to the next sentence.