RCall is a simple two-step process:

   1. Write the R script inside Julia's R macrostrings
   2. Copy the objects in R as objects in Julia

The documentation is just one page. 
http://juliastats.github.io/RCall.jl/latest/gettingstarted/

R has a massive collection in its Distributions Task View 
http://lib.stat.cmu.edu/R/CRAN/web/views/Distributions.html
Search (press F3) for 'stable' to find other packages.

If you're dealing only with draws from the Levy distribution (and not the 
whole family of stable distributions) 
you can do it in Julia: http://distributionsjl.readthedocs.io/en/latest/

using Distributions
x = rand(Levy(u, c), numSamples)

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