No, under US law, it is an "executive agreement", not a "treaty". The vast majority of US's international agreements are done as executive agreements, and not treaties; and the power of the executive branch to make executive agreements has been repeatedly upheld in the courts.
Specifically, there are two types of executive agreements:
- "Congressional-executive agreements". These are the ones that require changes to legislation to be implemented. Congress passes the needed legislation just like any other normal legislation, i.e. a majority of both houses of Congress. Most trade agreements are passed as congressional-executive agreements.
- "Sole executive agreements". These are the ones that do not require changes to legislation to be implemented. Congress is not involved at all.
This Iran nuclear agreement is a "sole executive agreement" because it does not require Congressional action to be implemented. (So it doesn't need to be passed by a simple majority by Congress.)
The President already has the legal authority to implement all of the US's obligations under the agreement, which are the relief of certain Iran sanctions. Some of those sanctions were implemented by the President, and which the President can remove by himself. Some of these sanctions were implemented by Acts of Congress, but those Acts specifically give the President the authority to waive them.
The Iran Nuclear Agreement Review Act of 2015 (the "Corker bill"), passed by Congress in May 2015, also confirms that "It is the sense of Congress that: [...] this Act does not require a vote by Congress for the agreement to commence;"
As to your question about whether something can "have the effect of a treaty if it's passed by a simple majority". The answer is yes (in the other way around). The Supreme Court ruled in the Head Money Cases that "treaties" (ratified by 2/3 of the Senate as specified in Article II) have the same legal effect in US law as regular legislation passed by Congress (by a simple majority of both houses), which means that Congress can modify or repeal (insofar as US law is concerned) any "treaty" that is ratified by the Senate, by passing a later law that contradicts it, just like it can with regular legislation. So, yes, any regular legislation passed by a simple majority (including for congressional-executive agreements) has the same legal effect as treaties.