My accountant tells me that he can't get me W-2 with only ITIN. I am authorized to work in the U.S. and am eligible for SSN but because of some mix-up between SSN office and USCIS, I haven't been able to get SSN yet.

IRS website doesn't address this issue and some online forum says it's not IRS rule but the computer software that doesn't allow it.

Any suggestions as to how I could get W-2?

Your advisor is correct an employer cannot except an ITIN for employment purposes. It is illegal and he can be penalized. This is why software is designed to not accept an ITIN on a W2.

You can confirm this by reading the W-2 instructions given to the employer, in the W-2 instructions, p.4, heading "Taxpayer identification numbers (TINs)". This document is on the IRS website, Internal Revenue Service. by searching for 'w 2 instructions".

Now understand, your accountant can never give you a W2, it is only given by an employer, after you have worked for him or her, (I assume your accountant is not your employer). It is designed to only show wages "already" earned.

Your employer, even if he is your accountant, however, can allow you to work and subsequently issue you a W2, as long as you are "eligible for a SSN, and have filed for one" , which you state you did. An ITIN isn't used as we stated earlier. However, your employer writes the words, "APPLIED FOR", instead of the SSN, (all zeros if filed electronically). Once you receive the SSN, he corrects the W2, by completing a W2c, which corrects the old one and shows the new SSN.
You get a copy. This information is found in Publication 15,p. 10, issued to employers on employment matters. This publication is available on the IRS website, Internal Revenue Service, use the search box, type "pub 15".

Your software program may not accept applied for or all zeros, in which case you may try filing by paper, but I suggest filing an extension, which is granted automatically till Oct.15.