You can use this op-amp based circuit:
The first two resistors will rise the voltage making it positive. Applying KVL and KCL you can easily see that if Vr is the voltage going to the non-inverting pin og the op-amp and Vi is the input voltage:
Vr=Vi+R1*(3.3-Vi)/(R1+R2)
then shifting -1.5V to zero means:
0=-1.5+R1*(3.3+1.5)/(R1+R2) from which
R1/(R1+R2)=1.5/4.8=0.3125 or 1+R2/R1=3.2 that is R2=2.2*R1
In this case when the input voltage reaches +1V we will have:
Vr=1+0.3125*(3.3-1)=1.719 V
In order to cover the whole dynamic range of the ADC (0-3.3V) we have to amplify by a factor:
Av=3.3/1.719=1.92
Using the op-amp in a non-inverting configuration as depicted in the image, the gain is
Av=1+R4/R3, then R4=R3*0.92
You can choose, now R1 much greater than the output impedance of you circuit; R1=10K should be OK, then R2=22K. Now you can choose arbitrary R3=18K then R4≈15K.
The actual tranfert function will be Vout=[Vi+R1*(3.3-Vi)/(R1+R2)]*(1+R4/R3) using the value just calculated:
Vout=1.89+1.2581*Vi
Don't forget to choose a single supply, rail to rail amplifier.