Rapture Envelope Problem

Is it possible to assign an envelope to the steps of the arpegiator in Rapture? ... With most synths the ADSR is triggered with each step.

Not in a direct sense. An arpeggiator takes incoming notes and reorders those events by an applied formula. Rapture has step generators.
These apply varying amounts of a control signal over separate parameters, like Pitch, Amplitude, Cutoffs, etc.

There's a step generator produced for every note played. The StepGen display represents common behavior across all note events.

I'd like each note to be staccato...not long.

There's a number of ways to do this; here's three of the choices. Keep in mind the separate control over Pitch and Amplitude.

Variation 1: The easiest to implement.

1). Load a wavetable (from the 'Empty' slot) to start with a basic sound.
2). In the Pitch StepGen, set up your Pitch sequence and turn the Status to On.
________{default settings: 16 steps spanning one octave, sync'd to 4 beats}.
3). Switch to the Amp modulator. Click on the Amp LFO waveform to advance to #7 (Saw Down).
4). Set the Amp LFO Status to On, Depth to 6.00, and Sync to 1/4.

Variation 2: Adaptable to each individual Pitch step.

1). Load a wavetable (from the 'Empty' slot) to start with a basic sound.
2). In the Pitch StepGen, set up your Pitch sequence and turn the Status to On.
________{default settings: 16 steps spanning one octave, sync'd to 4 beats}.
3). Switch to the Amp modulator. Click on the Amp LFO waveform to advance to #7 (Saw Down).
4). Set the Amp StepGen Status to On, and the steps to 4 (for example).
5). Right-click in the steps display, and select Copy Shape from LFO.
6). Change the Amp StepGen step count to 64. (16 Pitch steps X 4 Amp steps per 'envelope' = 64 steps required to line up.)

Variation 3: Most versatile for final envelope shape:

1). Load a wavetable (from the 'Empty' slot) to start with a basic sound.
2). In the Pitch StepGen, set up your Pitch sequence and turn the Status to On.
________{default settings: 16 steps spanning one octave, sync'd to 4 beats}.
3). Switch to the Amp modulator. Left-click in the AMP EG header, and set the Snap option.
4). Draw a three-point envelope in the shape of a right triangle.

• a) #0/2 (default) - time: 0.0 level: 0.000
  
• b) #1/2 (click to add) - time: 0.0 level: 1.000
  
• c) #2/2 (click to add) - time: 1000.0 level: 0.000

5). Hover over node #2/2, and press "S". Hover over node #0/2, and press "L".
6). Still in the Amp EG, set the Status to On, and the Sync to 1/4.

There's more methods. Some of the best results combine multiple modulation controls (LFO, EG, and StepGen) over the same destination.

Edit: Remember that in any modulator, Sync is tied to host tempo. Freq or Step are tied to note events. Freq cycles continuously; Shot plays the sequence or shape through only once. Step mode advances one step for every note event encountered. Most Status modes allow a choice between Sync (host) or Freq (note trigger).