You can take that measurement at any time. This is because right ascension moves along with the celestial sphere, so as an object moves from the east to the west, the right ascension value that it corresponds with also "moves". Much like longitude, even though the Earth rotates, the network of longitudes also rotates along with it.
Because of this, it might seem impossible to know how to figure out the right ascension at any given time, but luckily there are two values that help in this regard. These two values are
hour angle and
sidereal time.
Hour Angle is a measure that shows an object's relative position to the observer. Like RA, it ranges from 0h to 24h, with 0h at the star's highest point, 6h to the right, 12h at the lowest, and 18h to the left. In the following diagram, the circumpolar star would have an hour angle of 0h at its highest point and 12h at its lowest point:
Local sidereal time (LST) is a way of measuring time with regard to the stars. One full sidereal day is the time it takes for the Earth to completely rotate back to the same position of the stars. On Earth we typically use solar time to measure time, i.e. how long it takes for the Earth to rotate back to the same position relative to the Sun. However, since the Earth also
revolves around the Sun, it takes a little extra rotation to get back to the same position. Because of this, a sidereal day is shorter than a solar day. This diagram may be helpful, where 1 -> 2 is a sidereal day, and 1 -> 3 is a solar day:
Now how are these all related? Well luckily there is a simple mathematical relationship:
This really illustrates how the stars move through the sky. First, note that at any given sidereal time, the night sky will
always look the same. Even though the solar time might be drastically different, the stars' positions at the same LST will always have the same HA, since the stars must always have the same RA. At different times of any given night, the HA changes, but since the LST changes as well, the RA remains the same for any given star. Also, at different times of the year, the sidereal time at midnight will be different, but as you might know, the sky appears different at different times of the year, so when you account for hour angles, the RA is the same!
This can be a little difficult to really grasp, since there are so many times going around, so here's an example. Beta Cassiopeiae has a right ascension of about 0. However, let's say you're stargazing and you see it appears to the direct right of Polaris. This means that Beta Cas has a hour angle of 6, and so through the mathematical relationship, you can calculate the LST to be about 18:00 (since we don't want negative time). It doesn't matter what the solar time is, it could be 6 AM or 6 PM, but whenever the hour angle of Beta Cas is 6, the LST will always be 18:00. This makes Beta Cas helpful for finding sidereal time, since it is easy to find (it's the right-most star in the W/left-most star in the M) and has a RA of about 0.
This is probably way more than you wanted, or needed, to know. But basically, if you were to take that measurement, you can find the sidereal time, and then using the formula, calculate the hour angle, which is where in the sky you would expect it to be. This allows RA to be a standard coordinate for the entire world to use, without worrying about when the measurements are being taken.
Hope this helps!
