What I was taught in school was that it's acceptable to omit the comma when joining very short independent clauses. What's "short enough" is a judgment call.
I will happily agree with anyone that (a) it doesn't hurt to put the comma in, and (b) whenever the comma definitely makes things clearer, by all means it should be used.
In your particular case, my judgment is that your second independent clause is short enough that you could get away with omitting the comma. (I would include it, though.)
According to some authorities, such as Purdue OWL, yes, a comma should be used before "and" in that sentence:
Use commas to separate independent clauses when they are joined by any of these seven coordinating conjunctions: and, but, for, or, nor, so, yet.
It's a compound sentence, as you identified, and should therefore have a comma.
That being said, a more reasonable guideline, as given at Grammartips.homestead.com, governing comma use is that they, like all punctuation, should be used to reduce or eliminate ambiguity. You can often eliminate the comma
if both independent clauses are quite short, especially if the two clauses are very closely related, and even more so if the subject of both clauses is the same, or
if only the first clause is quite short, especially if the two clauses are very closely related, and even more so if the subject of both clauses is the same.
Here is an example involving two short clauses conjoined with 'but':
John went to the store but he didn't buy anything.
Best Answer
Use comma in that sentence.
This is the general recommendation for sentences with a dependent clause followed by an independent clause. In your sentence:
Dependent clause: If you can read this
Independent clause: [then] you might want to answer this question.
From the Wikipedia page on Commas:
Note that it doesn't mean that it is wrong to not use comma in this case. As noted by the same page: