Is the phrase "having a rave up" still in use?

I found the title of a 1965 album by the Yardbirds called Having a Rave Up quite funny when I first saw it. Dictionary.com defines "rave-up" as "a party, especially a wild one," and notes that this is an informal, British term. The reason it seems funny to me is because, although I have heard the term "rave" often, I have never heard "rave up" used.

Is this phrase still in use today, or is it something of a relic from the 60s–70s?

I'd suggest that it is — but not as frequently in the context of "rave-up" as you describe.

There is a genre of music, which I guess also exists outside of the UK, known as "rave music". This is an up-beat, electronic dance genre and people who listen to this music often attend "rave parties". Historically, these parties were underground and due to the attendees' drug use often organised illegally.

Over time, however, rave parties have become more mainstream.

In modern parlance you are likely to hear people say they "attended a rave" rather than "attended a rave-up", although if you said to me the latter, I would probably assume a boisterous party not necessarily linked to the rave genre.

All that said, if you said to someone today that you were at a "rave-up", they'd know what you meant.

According to the OED "rave-up" use is attested up to 1995, to mean

A lively party involving dancing and drinking.

Rave-up has a place in the 2012 edition of the Oxford rhyming dictionary.

Having a rave-up is mentioned in the 2013 book 16 songs about regret.

So "having a rave-up" is still an option in this day and age. I can imagine my parents saying.

It's in Urban Dictionary, so it can't be too old. Also, there is a Rave Up shop and a brand new Rave Up record label, which appears to be joining about three other Rave Up record labels in existence.

Also, there was another song "It's A Fast Driving Rave Up" by The Dandy Warhols that was popular in the 1990s, so it was at least still in recognizable use then.

A rave-up still has some use but it's most common, since around the 1990s, to simply say a rave. Rave-up is somewhat dated, and dates to 1967. Rave actually dates to 1960, but is more current and using rave-up sounds a bit like a not-with-it parent.

A search on the British National Corpus has only four results for rave up, but 55 for a rave: some are false hits like "rave group" or "rave review" or the related "rave party", but there's still a lot more than "rave up".