That can be due to bad connections at the cables, bad cables themselves, a tired starter, or an engine that's hard to turn over. All easy to test.
Before you replace the starter relay though, make darn sure it's bad, because chances are pretty high that the new one will be worse!
Unless you pay a high price for a USA made one, it's a crap shoot.
But check your cable connections, to make sure they're clean and tight. Disconnect them from their relative positions and clean any rust, paint or other blockage and re-attach.
If they are old, or worse yet, original(!) then just replace them with some 4 gauge, or better yet 2ga cables all the way around.
Make sure that the ground cable is attached directly to the engine block, and NOT an appendage somewhere else. The closer to the starter motor even, the better.
Make sure there is still a ground to the body. If the original cables have been replaced at least once, this is often overlooked by the installer.
Turn the motor over by hand like Broncobowsher was saying. Even if you are no longer testing the ignition, try to turn it over by hand to see if it's tight. This puts lots of strain on the starter.
If the engine is pretty grimy, I would even remove the distributor and clean the shank where it enters the block, and make sure that bore is clean too. This is overkill in most cases, but with a new-to-you but ancient rig, who knows how well things are connected.
Since the whole ignition relies on the good ground connection between the distributor body and the engine block, it's just good to know how clean it is.
Wasn't an issue 40 years ago, but now that these things are all closing in on 50 years old, these little things can make a difference.
And the next time you have it cranking you should have a timing light connected so you can verify the ignition timing is not too high. That will put strain on the starter as well.
Good luck.
Paul