First, you can use source without arguments to source the current buffer. As for Lua, it is better to use actual Lua code than calling Vim from Lua.

I was just about to supply a PR with this change, good I found that you'd already done it :)

I've tested this and it works well, and is the more Lua way of doing it in nvim.

Even more lua:

vim.api.nvim_create_autocmd("BufWritePost", {
  pattern = "lua/plugins.lua",
  callback = function(args)
    vim.cmd.source(args.file)
    vim.cmd.PackerCompile()
  end,
  desc = "Compile Packer plugins source.",
})

Nice, looks even better.

Even more lua:

vim.api.nvim_create_autocmd("BufWritePost", {
  pattern = "lua/plugins.lua",
  callback = function(args)
    vim.cmd.source(args.file)
    vim.cmd.PackerCompile()
  end,
  desc = "Compile Packer plugins source.",
})

It's not working for me:

Error detected while processing BufWritePost Autocommands for "plugins.lua":
Error executing lua callback: /home/susensio/.config/nvim/lua/user/plugins.lua:22: attempt to
 index field 'cmd' (a function value)
stack traceback:
        /home/susensio/.config/nvim/lua/user/plugins.lua:22: in function </home/susensio/.con
fig/nvim/lua/user/plugins.lua:21>

vim.api.nvim_create_autocmd("BufWritePost", {
  pattern = "lua/plugins.lua",
  callback = function(args)
    vim.cmd.source(args.file)
    vim.cmd.PackerCompile()
  end,
  desc = "Compile Packer plugins source.",
})

1. I think we want to use an autocommand group here, in case the file is sourced more than once.
2. I don't think that pattern will ever match because it isn't absolute and doesn't contain a wildcard (see :help autocmd-pattern).
3. Per the OP's original suggestion, we can omit the argument to vim.cmd.source().

So something like this:

vim.api.nvim_create_autocmd('BufWritePost', {
  group = vim.api.nvim_create_augroup('packer_compile', {}),
  pattern = '*/lua/plugins.lua',
  callback = 'source | PackerCompile'
})

I actually prefer to see a message when the command is executed. Also, */lua/plugins.lua might match a lot of files unintentionally, so I use the full path in the pattern:

vim.api.nvim_create_autocmd('BufWritePost', {
  group = vim.api.nvim_create_augroup('packer_compile', {}),
  pattern = vim.fn.expand('$HOME') .. '/dotfiles/vim/lua/plugins.lua',
  callback = function (ctx)
    vim.cmd.source()
    vim.cmd.PackerCompile()
    print('Packer compiled!')
  end
})