There's no phonemic contrast between /i/ and /ɪ/ in this context, and in fact the phonetic realization varies between the two and tends to lie somewhere in between:
In a syllable closed by /r/, there is no contrast in quality between a tense vowel and the lax vowel nearest to it. Consequently, as often happens in contexts in which there is no opposition between two sounds, the actual sound produced is somewhere between the two.
(A Course in Phonetics, 6th ed., Ladefoged & Johnson, p.99)
Since the contrast is neutralized and the vowel tends to lie between the two, we could reasonably indicate this sequence with either /i/ or /ɪ/. The traditional choice is /ɪ/, and that's what you'll find in most dictionaries that give AmE pronunciation in IPA.
But is that the best choice? Clark and Hillenbrand published a study in the Journal of the IPA in 2003 called Quality of American English front vowels before /r/. Although they did find that the NEAR vowel tends to lie somewhere between /i/ and /ɪ/, they found that overall it tended to be closer to /i/:
One major finding of the study is the stronger similarity of the high front vowels of hear and beer to /i/ than to /ɪ/. This similarity was evident in the acoustic measurements shown in the F1–F2 plots, in the discriminant analyses, and in the listening tests. If transcription is to accurately capture phonetic quality, [i] is a better choice than [ɪ] for representing the initial part of this diphthong, at least for this dialect most of the time.
(p.13, emphasis added)
But they also wrote:
On the other hand, the tendency of these vowels to fall in the /i/ territory is not absolute. Figures 1 and 2 show that many of the tokens lie intermediate between /i/ and /ɪ/ (consistent with the notion that the phonetic quality of the initial part of the diphthong is intermediate) and, as noted in the description of the listening results, several of the tokens excised from the diphthongs ending in [ɚ] were more strongly heard as /ɪ/, more so for hear than for beer, and more so for the men than the women talkers.
(p.13, emphasis added)
So although the convention is to transcribe this sequence with /ɪ/, you could make a reasonable argument that it's better transcribed /i/. Either way, there isn't a clear-cut choice between the two, so the choice of transcription comes down to a matter of convention.