She has a Psychology degree from Harvard. I'm fairly certain she knows her MBTI type. (And probably looks at the MBTI like most psychology people do... a variably problematic but anecdotal self assessment tool and conversation piece)
Why don't we just ask her?
According to a few websites out there that attempt to list celebrity MBTI tyoes, Natalie Portman is an INFJ.
However, I highly suspect these sites are nothing but conjecture as they list other celebrities as INFJs who can't possibly be: Johnny Cash (Quintessential ISFP), Zach Braff (ENTP posterboy), Nicholas Cage (SERIOUSLY?), Ashton Kutchner (ENTP extrordinaire), William Shatner (WTF?), Robin Williams (He's the freakin ENFP Avatar!), Emma Watson (INTP), Michelle Obama (I give up). Hell, these results don't even match their acting roles, let alone their public personas. Pure dart throwing conjecture.
I would love to have a lsit of celebrities who have actually taken the MBTI, and their self assessment results (individual percentages would be ideal).
Of course, it is possible that Natalie Portman self assessed as INFJ at some point, because a lot of the people on these lists have self identified as INFJs (even though some of them are most likely not INFJs ... these are their actual results) such as Nicole Kidman, etc. as well as the afore mentioned fact that Natalie Portman has a Psychology degree and has probably taken the MBTI as part of her classes. As further evidence of the possibility, Natalie Portman does seem to surround herself with ENTPs like Ellen DeGeneres, Zach Braff, and Andy Samberg.
She certainly seems to have INFJ body language in many of her roles. I have to agree that Black Swan was definitely an ISFJ role though. The Natalie rap was written by Andy Samberg, who is an ENTP, so this is likely the reason for the ENTP effect.
Here's my opinion...
Natalie has that classic Se inferior drive to do something physical to prove herself - dance, along with a lot of classic Se fails in interviews such as picking her nose.
Natalie is clearly an Fe in all of her interviews. Look up her Oscar acceptance speech, and you will see a profound amount of Fe. The degree to which she thanks people and what she says about them, their relationships, and how "We" and "us" oriented her focus is... very Fe.
Natalie has a strong Ti but with a clear focus on people (Fe) what she feels is right (Fe) with respect to her education in Psychology and philanthropistic endeavors, as well as learning several languages to a fair degree "...can speak two languages, Hebrew and English (her native languages), fluently. Also knows some conversational French, German, and Japanese and Spanish". This implies that her Ti is stronger than her Se, and that leaves ISTP and INFJ. Dominant or tertiary Ti.
Natalie is freakin brilliant in that way that an N dominant is freakin brilliant. She's also a big old nerd, just like us N types.
I met her at a Starbucks once, and while I didn't have the presence of mind to do much other than say stuff like "love your work" or ask her if she'd ever taken Myers Briggs, I really did get an INFJ vibe off of her. She was very sweet, down to earth, and warm. She talked to us for the few minutes we were in line about why she was in town (visiting family). She wasn't at all arrogant or anything you'd expect from a celebrity of her calibur. She seemed very much like my INFJ friends.