user19049: I want to make a candle flame light up triggered by a microcontroller. Is it possible? I only want to light it up. Not turn it down. Moreover, this is for a one-time use so the candle burning down and becoming shorter is not a problem. 

user16085: If you have a circuit, you can switch it on and off using a microcontroller.
So what you need is a circuit which can light a candle.  Have a look at these:
DIY arc lighter
CCFL Inverter becomes an Arc Lighter?
I predict your main problem will be dealing with the fact that candles get shorter as they burn.

user16673: Use two rods at either side of the candle, and engineer two motors to slide op and down these rods. Meccano kung-fu. 
Use limit switches to detect the highest and lowest positions for both motors. Mount a LED on one motor, and a laser (5 mW red is plenty). From the bottom, have both motors ascend, until the LED can receive data transmitted by the laser. Yes, you can most certainly use a laser diode for Serial.print. 
When at the right height, engage gasburner. You can use an LDR (shielded against light from the sides with heatshrink) to check if the candle has been lit - shortly after disengaging gasburner. You will need a reading prior to each ignition. 
Let me know how that works out.

user39333: Functioning proof of concept. 
Ni-chrome wire from hair dryer, approximately 2 Ohms, powered by 19 V for about 1 second. video of proof of concept. Lots to work out still, but this obviously can work.

user23822: A simple solution is too use nichrome wire which when a current is passes through it will heat up. You could wrap some of this wire around the wick on the candle and then power it either straight from your arduino or you could include a capacitor.
This is much safer than some of the other methods which use potentially dangerous high voltages.
I tested the nichrome wire approach and it works! See following video clip. 2 Ohm resistance and 19V for 1 second.  https://1drv.ms/v/s!AvcBubMtAczvifYZwoESAhUodOoqRA

19049: <p>I want to make a candle flame light up triggered by a microcontroller. Is it possible? I only want to light it up. Not turn it down. Moreover, this is for a one-time use so the candle burning down and becoming shorter is not a problem. </p>
 16085: <p>If you have a circuit, you can switch it on and off using a microcontroller.</p>

<p>So what you need is a circuit which can light a candle.  Have a look at these:</p>

<p><a href="https://www.youtube.com/watch?v=lk_1lzMiUVc" rel="nofollow noreferrer">DIY arc lighter</a></p>

<p><a href="https://www.youtube.com/watch?v=SK0p1PFiXI4" rel="nofollow noreferrer">CCFL Inverter becomes an Arc Lighter?</a></p>

<p>I predict your main problem will be dealing with the fact that candles get shorter as they burn.</p>
 16673: <p>Use two rods at either side of the candle, and engineer two motors to slide op and down these rods. Meccano kung-fu. </p>

<p>Use limit switches to detect the highest and lowest positions for both motors. Mount a LED on one motor, and a laser (5 mW red is plenty). From the bottom, have both motors ascend, until the LED can receive data transmitted by the laser. Yes, you can most certainly use a laser diode for Serial.print. </p>

<p>When at the right height, engage gasburner. You can use an LDR (shielded against light from the sides with heatshrink) to check if the candle has been lit - shortly after disengaging gasburner. You will need a reading prior to each ignition. </p>

<p>Let me know how that works out.</p>
 39333: <p>Functioning proof of concept. </p>

<p>Ni-chrome wire from hair dryer, approximately 2 Ohms, powered by 19 V for about 1 second. <a href="https://1drv.ms/v/s!AvcBubMtAczvifYZwoESAhUodOoqRA" rel="nofollow noreferrer">video of proof of concept</a>. Lots to work out still, but this obviously can work.</p>
 23822: <p>A simple solution is too use nichrome wire which when a current is passes through it will heat up. You could wrap some of this wire around the wick on the candle and then power it either straight from your arduino or you could include a capacitor.
This is much safer than some of the other methods which use potentially dangerous high voltages.</p>

<p>I tested the nichrome wire approach and it works! See following video clip. 2 Ohm resistance and 19V for 1 second.  <a href="https://1drv.ms/v/s!AvcBubMtAczvifYZwoESAhUodOoqRA" rel="nofollow noreferrer">https://1drv.ms/v/s!AvcBubMtAczvifYZwoESAhUodOoqRA</a></p>
