Is there any async equivalent of Process.Start?

Process.Start() only starts the process, it doesn't wait until it finishes, so it doesn't make much sense to make it async. If you still want to do it, you can do something like await Task.Run(() => Process.Start(fileName)).

But, if you want to asynchronously wait for the process to finish, you can use the Exited event together with TaskCompletionSource:

static Task<int> RunProcessAsync(string fileName)
{
    var tcs = new TaskCompletionSource<int>();

    var process = new Process
    {
        StartInfo = { FileName = fileName },
        EnableRaisingEvents = true
    };

    process.Exited += (sender, args) =>
    {
        tcs.SetResult(process.ExitCode);
        process.Dispose();
    };

    process.Start();

    return tcs.Task;
}

Here's my take, based on svick's answer. It adds output redirection, exit code retention, and slightly better error handling (disposing the Process object even if it could not be started):

public static async Task<int> RunProcessAsync(string fileName, string args)
{
    using (var process = new Process
    {
        StartInfo =
        {
            FileName = fileName, Arguments = args,
            UseShellExecute = false, CreateNoWindow = true,
            RedirectStandardOutput = true, RedirectStandardError = true
        },
        EnableRaisingEvents = true
    })
    {
        return await RunProcessAsync(process).ConfigureAwait(false);
    }
}    
private static Task<int> RunProcessAsync(Process process)
{
    var tcs = new TaskCompletionSource<int>();

    process.Exited += (s, ea) => tcs.SetResult(process.ExitCode);
    process.OutputDataReceived += (s, ea) => Console.WriteLine(ea.Data);
    process.ErrorDataReceived += (s, ea) => Console.WriteLine("ERR: " + ea.Data);

    bool started = process.Start();
    if (!started)
    {
        //you may allow for the process to be re-used (started = false) 
        //but I'm not sure about the guarantees of the Exited event in such a case
        throw new InvalidOperationException("Could not start process: " + process);
    }

    process.BeginOutputReadLine();
    process.BeginErrorReadLine();

    return tcs.Task;
}