Would a simple for loop work for this with the += compound operator?
By itself, no it wouldn't.
But some left shifts or some multiplies would sort it out.
Edit:
BE 1F A8 13.
Do you mean you want the sum of those values (0x198) in a 32 bit variable, or the value 0xbe1fa813 in a 32 bit variable?
Do you know the endianess of the input value?
uncompiled untested
unsigned long var = 0;
for int (int i = 0; i < 4; ++i) {
var <<= 8;
var+= array [i];
}