I have a player that used acid arrow and on the attack roll, crit fail. Do these types of spells still cause "on a miss" damage when a crit fail is rolled? 

I like to run my games RAW as much as possible. 

Acid arrow: A shimmering green arrow streaks toward a target within range and bursts in a spray of acid. Make a ranged spell attack against the target. On a hit, the target takes 4d4 acid damage immediately and 2d4 acid damage at the end of its next turn. On a miss, the arrow splashes the target with acid for half as much of the initial damage and no damage at the end of its next turn.

There isn't anything in the rules about that.  I'd say it's your call as DM.

Quote from Kyleh2486 >>

I have a player that used acid arrow and on the attack roll, crit fail. Do these types of spells still cause "on a miss" damage when a crit fail is rolled? 

I like to run my games RAW as much as possible. 

Acid arrow: A shimmering green arrow streaks toward a target within range and bursts in a spray of acid. Make a ranged spell attack against the target. On a hit, the target takes 4d4 acid damage immediately and 2d4 acid damage at the end of its next turn. On a miss, the arrow splashes the target with acid for half as much of the initial damage and no damage at the end of its next turn.

 Based on the wording of the spell, I’d say it’s meant to work like this: Bob casts Acid arrow at Frank. Bob rolls his ranged spell attack: 14+INT+Prof=Hit. Frank takes 10 damage(4d4) now and 7(2d4) at the end of his, Frank’s, next turn.

Or for a miss, Bob rolls 3+INT+Prof=miss. Frank takes 5 (half of the 4d4 result) now and nothing else at the end of his next turn.

For a nat 1, it guarantees the miss scenario, even if Frank’s AC were 1.

Unless you play with the common house rule where crit fails mean bad stuff for the attacker. Then a crit fail might go like “the spell partially backfires and you yourself take the other half of the damage Frank took from those 4d4.”

Quote from Stormknight >>

It's important to note that RAW there is no critical fail for attack rolls. The rules state:

If the d20 roll for an attack is a 20, the attack hits regardless of any modifiers or the target's AC. This is called a critical hit, which is explained later in this chapter.

If the d20 roll for an attack is a 1, the attack misses regardless of any modifiers or the target's AC.

As you can see, rolling a natural one on the d20 is just an ordinary miss, but one that occurs no matter how good your attack bonus is, or how low the target's AC is. It's just a miss. :)

Makes sense. Thanks!