Pattern.compile("\\(([^)]+)\\)");

The Pattern is always the same so you may just as well make it a private static final constant. This will avoid having to recompile the pattern each time.

Arrays.asList(/*..*/).stream().collect(Collectors.toList());

Why this dance? Arrays.asList returns a List. You only do a stream on the return result.

    final List<String> list = Arrays.asList(matcher.group(1).split(","));
    list.stream().forEach(a ->
    {
        final String[] ar = a.split("->");
        map.put(ar[0], ar[1]);
    });

However a Pattern an return a Stream split according to the pattern directly:

Pattern COMMA_PATTERN = Pattern.compile("\\s*,\\s*");


COMMA_PATTERN.splitAsStream(matcher.group(3)).forEach(a ->
{
    //...
}

You can use a single match of a Pattern to find both the leading values and the string inside the parenthesis:

private static final Pattern FULL_PATTERN = Pattern.compile("^(\\$\\w+)\\s*=>\\s*(\\w+)\\s*\\(([^)]+)\\)$");
private static final Pattern KEY_VALUE_PATTERN = Pattern.compile("(\\w+)\\s*->\\s*(\\w+)");
private static final Pattern COMMA_PATTERN = Pattern.compile("\\s*,\\s*");

public static Macro getMacro(String str) {
    final Macro macro = new Macro();
    final Map<String, String> map = new HashMap<String, String>();
    final Matcher matcher = FULL_PATTERN.matcher(str);
    if(!matcher.matches()) {
        throw new IllegalArgumentException("...");
    }

    COMMA_PATTERN.splitAsStream(matcher.group(3)).forEach(a ->
    {
        final Matcher kvMatcher = KEY_VALUE_PATTERN.matcher(a);
        if(!kvMatcher.matches()){
             throw new IllegalArgumentException("...");
        }

        map.put(kvMatcher.group(1), kvMatcher.group(2));
    });
    macro.setMap(map);
    macro.setKey(matcher.group(1));
    macro.setType(matcher.group(2));
    return macro;

}

You'll note I added \\s* to various points in each pattern, This lets you ignore the whitespace that may surround the operators.

The \\w in a Pattern means a word character. If you only want alphanumeric +undescore then you'llneed to replace each instance of it with [\\p{Alnum}_]