Currently the best you can do is to build a somewhat unwieldy relocatable “bundle” with PackageCompiler.jl [1], but there are apparently plans for actual static compilation using an approach more similar to that used in GPUCompiler.jl [2], and the latter approach should as far as I understand allow for the creation of proper .so/.dlls.
[1] https://github.com/JuliaLang/PackageCompiler.jl
[2] https://github.com/JuliaGPU/GPUCompiler.jl