Absolutely NO WAY. The dryer is not going to work on a 20A circuit of any form. It will typically want a 230V 50A circuit. Further, that is an obsolete plug for the dryer anyhow. In some cases, it may be legal if you have a similar receptacle to plug it into. In other cases (where there is a four-pin receptacle required by modern codes, you'll need to replace the entire cord for the machine with one with four wires and a matching four pin plug.

It is a 3 prong range cord. Most dryers are 30Amp, but I have seen range cords and receptacles used for dryer. A range cord typically means 50A but the dryer really uses 30A. If the breaker for that circuit is 30Amp and you have the receptacle to match the cord where the dryer will go then it is usable. Obviously if you think you can use a magic adapter to wire it to a standard 20A circuit you have a lot to learn. It is a completely different type of circuit, double pole vs single pole, and it will trip the 20A breaker every use. There is no adapter available for such an idea for those reasons.

You need a new properly sized electric run (most likely 10 gauge) and a 4 prong dryer receptacle and a 4 prong dryer cord. Check the specs of the dryer and the breaker size for correct wire gauge and breaker. Typical is 30A and 10ga.

That is a 3 prong 30 amp 125/250V dryer cord.

Fred wins :P Bookmarked awesome diagram for future use. In my defense the 50A looks pretty similar!