No, as the Non-Custodial Parent, you will need a signed Form 8332 from the Custodial Parent of your Child in order to claim them.
In addition, your Ex-Wife's legally separated husband cannot claim the child as a Dependent unless he receives a signed Form 8332 from her as well. If they are still legally married, per IRS rules, the child is his legal child also.
So basically, if your Ex-Wife is the Custodial Parent of your Child, she can determine who can claim the Child if she chooses not to by filling out Form 8332 and giving it to that person to attach to their Tax Return.
You can check our Form 8332 & the Instructions here: https://www.irs.gov/pub/irs-pdf/f8332.pdf.