No, this usage of the apostrophe is incorrect.
Using an apostrophe when a trailing -e of nouns or certain verb forms has been omitted is not listed under § 96 of the official orthography rules and therefore it is generally not a valid usage of the apostrophe.
There is an exception if the word might otherwise be hard to understand or ambiguous, such as in the example mentioned by Tofro:
Das Wasser rauscht', das Wasser schwoll.
Here, the apostrophe makes it clear that the verb is in preterite form (rauschte with an ommitted trailing -e), not present (rauscht).
Using an apostrophe in a contraction like the following is correct:
Ich sag's dir.