How close is AES to random oracle model? I'm wondering if there are any guarantees about AES's randomness in comparison to Random Oracle, but I couldn't find any papers nor publications about it.

Let's say I have a blackbox B which for any input returns either encryption or random data

B(input){  
  if(hasBeenEncryptedBefore(input)){
     fail();
  }
  with prob. 0.5 returns: "truly random bits from ROM" OR "f(input)"
}


where:

f(input){
  IV := randomIV();
  key := getKey();
  return IV, AES_ENC(IV, key, input);
}


let's assume that getKey() returns the same key for each encyption and randomIV() returns truly random bits from ROM

Is the adversary interacting with B able to determine whether the result comes from ROM or AES?
Like all PRNGs (pseudo random number generators), there can be no guarantee of randomness, so therefore no statement to that effect can exist. However, reasonable randomness for a given application can often be demonstrated.

Following up on Daniel Lemire's work: I used 254 p-values (30 corrected) obtained from each of over 512 TestU01 BigCrush results on high and low 32-bits (forward, reversed and byte reversed) of the 64-bit output to perform a (work-in-progress) meta-analysis of AES in counter mode (seeded using SplitMix). I find no evidence that suggest any issues with AES, however BigCrush (thus my meta-analysis) has its limitations.

I believe others (perhaps Vigna/Blackman) have performed Hamming Weight Dependency analysis on it to over a petabyte, but cannot find documentation.

Wikipedia has an AES article with information on security, which is a related topic.