The settled part
Across noon positions from 1930 to 2035, the Sun on 12 January falls between about 21.1 and 22.5 degrees of Capricorn. That range holds within a degree and a half over more than a century because the leap year rule cancels the calendar's six hour annual slip against the orbit.
Twenty one degrees places the birthday in the third decan, the band from twenty to thirty. The Chaldean order gives that band to the Sun and the triplicity scheme gives it to Virgo, and so to Mercury. Both attributions are traditional and they are read as brightness under restraint and as method under restraint respectively.
The sign is not in question at any point. Aquarius begins when the Sun completes thirty degrees of Capricorn, around 19 or 20 January, which is a week of travel away from this date. No birth hour or time zone closes a gap of that size.
The Moon depends on the hour
The Moon covers roughly thirteen degrees a day, close to half a sign. On any given 12 January it will be in one sign for part of the day and quite possibly the next for the rest, and in years where a sign change falls near midnight three signs are technically in play across the calendar date.
This is not a marginal detail. The Moon is the second most quoted placement after the Sun and the one most often reported wrongly, because people supply a date and no time and the calculation quietly defaults to noon.
A defaulted Moon is the most common error in a chart drawn from partial information, and it is invisible, because the result looks exactly as confident as a correct one. The only signal is whether a time was supplied.
The rising sign depends on the hour and the place
The whole zodiac passes the eastern horizon once every twenty four hours, so a new sign begins rising on average every two hours. The intervals are not equal, because the angle of the ecliptic to the horizon changes with latitude, and some signs rise much faster than others at high latitudes.
That means the rising sign needs a time and a town, not a date. Without them it can be any of the twelve, and any page that assigns one from a birthday alone is guessing.
Working out the rest
The order of operations is simple. The date gives the Sun. The time gives the Moon exactly and gives the Ascendant. The birthplace fixes the time zone, which corrects both, and sets the latitude, which shapes the houses.
The widget above handles the first step properly, computing your solar degree from your own year and birthplace instead of assuming noon, naming the decan, and reporting how far your Sun sits from the nearest sign boundary. On 12 January that distance is a comfortable one in both directions.
The tradition itself has always worked this way. The Sun is one significator among several and the older texts spend far more attention on the Ascendant and its ruler than on the sun sign, which is a comparatively recent centre of gravity.
Questions people ask about this
What sign is 12 January?
Capricorn, every year. The Aquarius boundary arrives around a week later, well out of reach of any birth hour or time zone.
What degree and decan is 12 January?
About 21.1 to 22.5 degrees of Capricorn at noon across 1930 to 2035, which places the birthday in the third decan, the band from twenty to thirty.
Can I find my moon sign from the date alone?
Sometimes, if the Moon happens to stay in one sign for the whole of that calendar day in your year. Often it does not, and then the birth hour is what decides it.
How accurate is a rising sign without a birth time?
It is not a rising sign at all, only a guess. The Ascendant changes roughly every two hours, so a date on its own narrows it not at all.
Does the time zone really matter?
Yes. Positions are computed from a universal instant, so a local clock time has to be converted before anything is calculated. Getting the zone wrong shifts everything by hours.
Who rules the third decan of Capricorn?
The Sun in the Chaldean order and Mercury, through Virgo, in the triplicity scheme. Saturn continues to rule the sign itself regardless of the decan.