The OP has not defined his word, "belong", so I will take it in three senses:
- Chronology of Story
I have made the case here >> When did the story of Ruth take place? that the story of Ruth belongs to the time BEFORE the Hebrew monarchy, ie, during the time of the Judges.
- Time of Composition
The time of composition is completely unknown and the author is also unknown. Any attempt to determine such (and there have been many) are entirely speculative. All that can be said is that it must have been completed during or after the time of King David's reign.
- Position in the Canon
It is well-known that the position of a piece of writing in the Canon of books composing the OT has nothing to do with either its time of composition, it author or its story history. Therefore, nothing can be deduced from Ruth's position in either the Hebrew Bible, the LXX or the Latin Vulgate. To illustrate this, I list the various book orders in these ancient texts:
Hebrew canon (Biblical Hebraica):
- Pentateuch
- Joshua & Judges
- Samuel & Kings
- Isaiah
- Jeremiah
- Ezekiel
- 12 Prophets
- Psalms
- Job
- Proverbs
- Ruth
- Song of Songs
- Ecclesiastes
- Lamentations (of Jeremiah)
- Esther
- Daniel
- Nehemiah
- Chronicles
Septuagint (LXX) [Note: this order is not uniform but this is the most common.]
- Pentateuch
- Joshua & Judges
- Ruth
- Samuel & Kings
- Chronicles
- Esdras
- Ezra & Nehemiah
- Tobit, Judith
- Esther
- Maccabees
- Psalms
- Prayer of Manasseh
- Job
- Proverbs
- Ecclesiastes
- Song of Songs
- Wisdom
- Sirach
- Psalms of Solomon
- 12 prophets
- Isaiah
- Jeremiah
- Baruch
- Lamentations
- Letter of Jeremiah
- Ezekiel
- Daniel
Latin Vulgate of Jerome
- Pentateuch
- Joshua & Judges
- Ruth
- Samuel and Kings
- Chronicles
- Ezras
- Tobit
- Judith
- Job
- Psalms
- Proverbs
- Ecclesiastes
- Song of Songs
- Wisdom
- Isaiah
- Jeremiah
- Lamentations
- Ezekial
- Daniel
- 12 Prophets
- Maccabees
It is immediately clear that the order of books has little to do with its historical content nor the time of its composition, else the order would be the same. The Hebrew and LXX text-book orders were complied at a similar time in history (the Latin text was a little later than these two). Thus, the position of Ruth appears to matter very little.
English Bibles mostly follow the Vulgate order.
My personal preference is the position it has in in the LXX and Vulgate because it is history from the time of the Judges. The author and time of composition is unknown so attempting to place it order of composition is fraught. By contrast, the LXX and Vulgate have a simpler arrangement of:
- Pentateuch
- History
- Poetry
- Prophets