I was told that the tilde (˜) means "approximately." Is this true?
Very few sources say that writers can use the tilde to mean "approximately." Merriam-Webster OnLine is the one source that we found that actually endorses the use of the tilde to mean "approximate value," but even then this use is reserved for mathematics. This source also notes that the tilde is used to represent negation in logic.
Because your readers could interpret the tilde in many different ways, you should use the tilde to mean "approximately" only in math-related contexts. Readers who are mathematically inclined are more likely to understand the meaning.