Article I, Section 9, Clause 7: No Money shall be drawn from the Treasury, but in Consequence of Appropriations made by Law; and a regular Statement and Account of the Receipts and Expenditures of all public Money shall be published from time to time.
While there may be no specific mention of such "giving" as you say, there are very specific instructions on how to constitutionally appropriate public monies for unspecified reasons.
I can guarantee you, that at the bottom of the idea of foreign aid, the proper constitutional steps were taken.
I can guarantee you that they were not.