If I am given corporate housing will I have to pay taxes on it? It will be for a short term project relocation. If I do not take the housing I will not get the job.

• Exception: It can be non-taxable if it meets the IRS’s “convenience of the employer” test (IRC §119):
  
1. On the business premises – The lodging must be on or near the employer’s place of business.
2. For the employer’s convenience – Provided for business reasons, not just as extra compensation.
3. Condition of employment – You must be required to accept the lodging to properly do your job.
•  

I concur with Bsch4477's answer, it is most likely not taxable for the reason's stated.

But, the bottom line may be how your employer handles it at W-2 time. If they do not include the value of the housing in box 1 of your W-2 (and they most likely won't), the housing value is not taxable to you. 

Q. Is this  nontaxable fringe benefits per Pub FB-15?

A. Maybe, depending on other details. More likely,  this is the employer directly paying out of town business expenses.  Either way, it should not be taxable to you. 

@macey.karr , agreeing with the excellent / complete answers by my colleagues @Bsch4477  and @Hal_Al , just like to draw attention to the assumption here  that this housing is in the USA and not abroad  and that the  short time is less than a year.

It is in the US!