Here is a fast version with zero allocations. You can also control the output through the optional argument s. If the array has more than 63 elements, you can set s = 0.0 or s = big(0) to avoid Int overflow.
function bitarr_to_int5(arr,s=0)
v = 1
for i in view(arr,length(arr):-1:1)
s += v*i
v <<= 1
end
s
end
arr = BitArray(rand(0:1,50))
@btime bitarr_to_int($arr)
@btime bitarr_to_int2($arr)
391.547 ns (2 allocations: 992 bytes)
51.622 ns (0 allocations: 0 bytes)