FastTransforms.jl v0.2.2 includes nonuniform fast Fourier transforms thanks to Alex Townsend:

nufft1
assumes uniform samples and noninteger frequencies; 
nufft2
assumes nonuniform samples and integer frequencies; 
nufft3 ( = nufft)
assumes nonuniform samples and noninteger frequencies; 
inufft1
inverts annufft1
; and, 
inufft2
inverts annufft2
.
Basic usage is like so:
julia> Pkg.add("FastTransforms")
julia> using FastTransforms
julia> n = 10^4;
julia> c = complex(rand(n));
julia> ω = collect(0:n1) + rand(n);
julia> nufft1(c, ω, eps());
julia> p1 = plan_nufft1(ω, eps());
julia> @time p1*c;
0.002383 seconds (6 allocations: 156.484 KiB)
The new algorithms are described in the following preprint:
D. Ruiz—Antolín and A. Townsend. A nonuniform fast Fourier transform based on low rank approximation, arXiv:1701.04492, 2017.