Can I initialize a C# attribute with an array or other variable number of arguments?

Attributes will take an array. Though if you control the attribute, you can also use params instead (which is nicer to consumers, IMO):

class MyCustomAttribute : Attribute {
    public int[] Values { get; set; }

    public MyCustomAttribute(params int[] values) {
       this.Values = values;
    }
}

[MyCustomAttribute(3, 4, 5)]
class MyClass { }

Your syntax for array creation just happens to be off:

class MyCustomAttribute : Attribute {
    public int[] Values { get; set; }

    public MyCustomAttribute(int[] values) {
        this.Values = values;
    }
}

[MyCustomAttribute(new int[] { 3, 4, 5 })]
class MyClass { }