While the top answer with "Fass!" is correct, the proposed translation into english in the comments as "Catch!" is horrible. "Apprehend" is what people mean to say.
"Catch!" would be "Fang!" in German and it's something you'd say if you throw a ball for the dog. Catching is getting something that is given to you. "Fassen" on the other hand, implies taking possession of something.
"Apprehend" is thus too elevated as a translation. "Grab!" dwells too much on the moment of contact, ignoring the chase. "Catch!" is too passive.
- You're catching fish that end up on your hook. The ones that
don't, are free to swim about. A shark isn't catching fish. It's
hunting them down.
- You catch a cold - you never meant to. Goes away.
- You catch a ride/cab - the driver cooperates with you. Later drives away.
- You catch a wave - it has to come along. Goes away.
- You catch a ball - it's thrown at you. You give it away while playing.
- You catch a glimpse - fate plays into your hands, it's gone the next moment.
- You catch a butterfly... it's childsplay and you still might want to let it go.
Catching a thief is the same: You catch him, because he's there to be caught. His lameness plays into your hands. You're also not gonna keep him.
Taking ahold of a thief in contrast implies somewhat more effort on your part, resistance on his part.
Police are catching thieves in the sense that they as an institution or person of authority are in the luxurious position of only having to "catch" things. It's a low effort thing in a sense since that they overpower thieves by default, being the police: tactically, backups, training, weapons, strategy...
Now, getting a thief sounds more like a hustle was involved. )
Fassen - in general would be best translated as "Getting a grip" or "Getting a hold on smth." A translation for "Brace yourself" would also be using this word in German.
- Go get ahold of him! - also known as "Get him!"
Another thing against saying "Fang!" is that in contrast "Fass!" has this "Obtain and contain" nuance to it. Take it and keep it... While "Catch!" doesn't care if you spit out the ball right after you caught it. Meanwhile the word "fassen" in german is related to the word "fest" meaning tightly, securely.
One more thing: one could also say: "Fass ihn!" adding the "him" explicitly. But only saying "Fass!" makes the command less about "catching someone" and more about the "go getting" per se. So bottom line, an accurate translation would be: "Go get (it)!" or "Apprehend!". For those who are wondering the "go" is hidden within the imperativness. Edit: "Get" alone has the potential of passivity, just as "catch", like in "getting gifts". I guess "go getting" might be idiomatic ?
This de-personifies the whole thing. It's now less about a person being hunted down, possibly getting hurt, it's a process for the dog to be executed that we are talking about. It's raw and cruel. You're also talking to an animal telling it to do the impossible: "go get a grip on him". So you're not responsible for the punctures and ruptures - you only asked for a grip. We'll just ignore the part with your hunting instinct and your sharp teeth.
Also on the pronunciation, I have a hard time believing the correct IPA is "fas". It should rather be "fass" and this is important because without dwelling on the "s" your "command voice" is not only pretty anemic but you might place emphasis on the "a" which is completely wrong.