I am not the executer of my father’s Will, can I request a copy of it?

The Will will have to be entered into probate. At that point, any beneficiaries should be notified of their inheritance. If you are a bendficiary you can request a copy of it; if you have not been notifiedthen possibly you weren't left any bequest. The fact is that children have no automatic inheritance rights under a Will. 

That having been said, once the Will is filed you can see a copy of it whether or not you are a beneficiary; it is a matter pf public record.  Simply go to the Probate Court in the county in which your father was domiciled at the time of his death; it would be filed there.  

Note:  You should also be aware that certain assets can be transferred outside of probate.  For example, if your father had a small estate, property may have been transferred by affidavit.  Further, some assets may have been held as "joint tenants with right of survivorship", in which case the other joint tenant would have received your father's share of property operation of law. Also, funds in an IRA, pension, 401(k), or other retirement plan also by-pass probate and go directly to the named beneficiaries.  Additionally, the same holds true for any life insurance proceeds.